Course Title  Lead Instructors  ECTS credits  Course Code 

Academic Communication: Preparatory English for Phd Exam
Efficient professional communication is the key to Academic success. The course is designed for PhD students who want to maximize their academic potential by boosting their ability to write research papers, present in front of multidisciplinary audiences, participate in scholarly discussions and engage in other forms of academic communication.
The main goal of the course is to enable PhD students to produce clear, correct, concise and coherent texts acceptable for the international professional community. The course serves as a preparation for the qualification language exam, which is a prerequisite for the Thesis defense. 
Elizaveta Tikhomirova  3  PE03029 
Academic English (for GUAP Students)
Proficient communication in English is essential for a successful academic career in a multinational environment. The course provides insight into relevant aspects of text structure, grammar, vocabulary, and style building the framework of academic communication.
Students will develop essential writing and presentation skills, and get ample practice in various forms of scholarly discourse, such as writing research papers, making presentations with visual aids, and taking part in scientific discussions. 
Elizaveta Tikhomirova  3  ME03028 
Academic Writing (Theory and Practice)
The ability to use proper English for professional purposes is becoming more and more urgent nowadays. Planning, writing, revising and editing your own work in a lingua franca of modern science is one of the key skills a scientist should have. The aim of the course is to help the students plan the written work (a paper/ a thesis), understand its major parts and the language typical of them. The course will familiarize the students with major problems the Russian authors have in the English formal writing as well as the ways to overcome them. Extensive writing, self and peer editing and getting feedback from the lecturer will provide grounds for future autonomous writing.

Anastasiia Sharapkova  3  ME03027 
Advanced Molecular Biology Techniques 1
This projectbased course provides experience with scientific project planning and implementation in the molecular biology/biotechnology lab. Coursebased research projects are geared towards the background and experience of students.The goal of the course is to teach students good laboratory practice and rational planning of the experimental work.

Konstantin Severinov  6  MA06046 
Applied Methods of Analysis  Khoroshkin  3  ME06013 
Asymptotic Methods in Complex Analysis
In this course, students encounter a range of asymptotic methods, good for evaluation of ordinary and path integrals, solving linear and nonlinear differential equations with corresponding connection problems. Most of the techniques are motivated by examples from theoretical physics (quantum mechanics or quantum field theory). We start from formal construction of asymptotic series, proceed with resummation techniques and their applications to constructing solutions to nonlinear ODEs. Next, we discuss asymptotic matching techniques, including nonlinear connection problems. Finally, we discuss approaches to asymptotic evaluation of path integrals.

Tikhonov  3  MA06275 
Computational Science and Engineering III: Fast and Efficient Solvers
Partial differential and integral equations play a key role in modelling of modern physical and engineering applications. Problems arising in these applications often require largescale computations, so fast and efficient methods have to be used. This course is devoted to modern algorithms that have nearlinear time complexity for largescale partial differential and integral equations. Course topics include fast multipole method and hierarchical lowrank matrices, highfrequency problems, multigrid and domain decomposition methods. Examples of applications include aircraft modelling, MRI, electronic structure computations and acoustics.

Ivan Oseledets  6  MA06227 
Differential and Symplectic Geometry  Maxim Kazaryan, Sergei Lando 
3  MA06175 
Dynamical Systems and Ergodic Theory
Dynamical systems in our course will be presented mainly not as an independent branch of mathematics but as a very powerful tool that can be applied in geometry, topology, probability, analysis, number theory and physics. We consciously decided to sacrifice some classical chapters of ergodic theory and to introduce the most important dynamical notions and ideas in the geometric and topological context already intuitively familiar to our audience. As a compensation, we will show applications of dynamics to important problems in other mathematical disciplines. We hope to arrive at the end of the course to the most recent advances in dynamics and geometry and to present (at least informally) some of results of A. Avila, A. Eskin, M. Kontsevich, M. Mirzakhani, G. Margulis.
In accordance with this strategy, the course comprises several blocks closely related to each other. The first three of them (including very short introduction) are mainly mandatory. The decision, which of the topics listed below these three blocks would depend on the background and interests of the audience. 
Aleksandra Skripchenko, Anton Zorich 
3  MA06257 
Efficient Algorithms and Data Structures
Design and analysis of algorithms and data structures is a core part of Computer Science and is of fundamental importance to all application areas. The goal of this course is to provide a representative sample of advanced algorithmic notions and techniques that constitute a modern “toolbox” for solving reallife problems. We will mainly deal with basic discrete objects – sets, trees, graphs, strings, … – and present efficient data structures and algorithms for solving various basic problems on these objects. Therefore, this course can be viewed as a basis for more specialized subjects. Lecture part of the course will focus on principles and ideas as well as on their mathematical justification. The practical part will be devoted to exercises and developing practical problem solving skills.

Gregory Kucherov  3  MA03270 
Energy Colloquium
The Energy Colloquium educates the audience in the presentday research and applications within the broader field of Energy Science and Technology. The Colloquium consists of a series of presentations by invited academic and industry speakers. The presentations target a nonspecialist audience.
All Master and Ph.D. students within the Energy Program are encouraged to attend the Energy Colloquium during the entire period of their studies. Students can earn 1 credit, if he/she participates in the Energy Colloquium over the course of any 2 terms of the academic year. Students who passed one round can make next (for credit) over the course of their subsequent studies. 
Alexei Buchachenko  1  MA04092 
Energy Systems Physics and Engineering
This course will provide a graduate level overview of modern energy systems, covering generation, conversion, transportation and enduse energy technologies. The application of principles of thermodynamics, heat and mass transfer to energy systems is explained and foundation for modern energy conversion technologies is given. A special emphasis will be given to improving students’ ability to extract wellformulated physics and mathematics problems from energy systems reality.

Aldo Bischi  6  MA06001 
Experimental Data Processing
The course introduces students to practically useful approaches of data processing for control and forecasting. The focus will be on identifying the hidden and implicit features and regularities of dynamical processes using experimental data. The course exposes data processing methods from multiple vantage points: standard data processing methods and their hidden capacity to solve difficult problems; statistical methods based on statespace models; methods of extracting the regularities of a process on the basis of identifying key parameters. The course addresses the problems in navigation, solar physics, geomagnetism, space weather and biomedical research and will be useful for broad range of interdisciplinary applications.

Tatiana Podladchikova  6  MA06238 
Geometric Representation Theory
Geometric representation theory applies algebraic geometry to the problems of
representation theory. Some of the most famous problems of representation theory were solved on this way during the last 40 years. The list includes the Langlands reciprocity for the general linear groups over the functional fields, the LanglandsShelstad fundamental Lemma, the proof of the KazhdanLusztig conjectures; the computation of the characters of the finite groups of Lie type. We will study representations of the affine Hecke algebras using the geometry of affine Grassmannians (Satake isomorphism) and Steinberg varieties of triples (DeligneLanglands conjecture). This is a course for master students knowing the basics of algebraic geometry, sheaf theory, homology and Ktheory. 
Mikhail Finkelberg  3  MA06271 
Graphical Models of Statistical Inference
This course is recommended for IT students, as well as other specialization students (e.g. Energy & Bio), interested in learning about modern theoretical and practical approaches to analysis of big data sets with reach statistical correlations expressed through graphs, matrices, tensors and related. The course is light on rigorous proofs, but rich on statistics and physics intuition.
The course may be considered as a "special chapter" extension of "Stochastic Modeling & Computations". 
Michael Chertkov  3  MA03135 
Hamiltonian Mechanics
This is the first among the base courses in the theoretical physics, aimed for the master
students. Matematical methods of modern theory of Hamiltonian systems are based on the concepts, The preliminary program of the course includes: 
Andrei Marshakov  3  MA06174 
Industrial Robotics
The Industrial Robotics course teaches some basic to advanced knowledge about industrial robots. When someone hear about industrial robots most of them imagine a robot arm which is welding something or working in a production line in a factory. Industrial robots have a wide range of activity in the present world and Their application is increasing day by day. In this course we consider the subsystems of the robot including mechanical parts, sensors, actuators and end effector tools and describe all type of choices and their advantages. Forward and Inverse kinematics and Rigid body dynamics will be described in this course. We talk about control architecture of industrial robots and describe industrial networks. Programming the robot and programming languages for commercial robots will be considered and introduction of collaborative robots. Experimental work with real industrial robots which are in the lab is the practical part of this course. Performing the laboratory works give the knowledge to how to work with industrial robots, increase your programming skills and give you the opportunity to make your own application with robots.

Fardad Azarmi  6  MA06249 
Innovation Workshop
Innovation Workshop is a full time monthlong course with the threefold purpose: to create a foundational experience in E&I for all, to empower the students to identify and solve realworld problems with technology, and to instill an entrepreneurial “cando” attitude in the culture of the student cohort. Students engage in experiential learning to prototype the entire technology innovation "cycle", progressing from idea to product/prototype. The participants iterate all the components of an innovation: the problem to solve, the technology to solve it, the opportunity for impact, and the vehicle to bring the proposed innovation to life. The course puts together social, business, technological and scientific aspects of innovation in intense, handson setting. The course is less about knowledge and more about developing skills and attitudes, necessary to lead successful life in innovation.

Ilia Dubinsky  6  MC06001 
Innovation and Intellectual Property Studies Doctoral Seminar
This course is a compulsory academic seminar series for all Ph.D. students in the Innovation and Intellectual Property Management Ph.D. Program. It consists of weekly research seminars that address the state of the art in research about the role of intellectual property in technological innovation. Specific topics and themes in the course will vary from year to year, but will typically include: theories of innovation; concepts and theories in IP management; practical issues in IP management; case studies in IP strategy; valuation of IP; Russian and international trends in intellectual property law; topics in technology entrepreneurship; product development and new technology; IP and design; patent analytics for innovation research; commercialization strategies of technology startups; organizational issues in technology innovation; conceptual issues at the interface of technology, science and business; public policy for technology, science and innovation; ethical and social issues related to IP and technological innovation; case studies in innovation management; philosophy of technology and philosophy of intellectual property; theory and methodology in IP management research; technology transfer and commercialization of university research; international collaboration and international trade in technology. As part of their seminar obligations, all students must prepare a formal written research paper on a topic that may or may not be directly related to their thesis research and make a presentation about the paper to the seminar group. The paper will be assessed.

Kelvin Willoughby  special  PC06009 
Integrable Systems 2
The course is devoted to quantum integrable systems. The history of quantum integrable systems starts from 1931 when
H.Bethe managed to construct exact eigenfunctions of the Hamiltonian of the Heisenberg spin chain with the help of a special substitution which became famous since that time (ansatz Bethe). In one or another form this method turns out to be applicable to many spin and fieldtheoretical integrable models. From the mathematical point of view, Bethe's method is connected to representation theory of quantum algebras (qdeformations of universal enveloping algebras and Yangians). Here is the list of topics which will be discussed in the course. – Coordinate Bethe ansatz on the example of the Heisenberg model and – Bethe ansatz in exactly solvable models of statistical mechanics – Calculation of physical quantities in integrable models in thermodynamic – Bethe equations and the YangYang function, caclulation of norms of Bethe – Quantum inverse scattering method and algebraic Bethe ansatz, quantum Rmatrices, – Functional Bethe ansatz and the method of Baxter's Qoperators, functional The knowledge of quantum mechanics and statistical physics for understanding of 
Anton Zabrodin  3  ME06010 
Introduction to Data Science
The course gives an introduction to the main topics of modern data analysis such as classification, regression, clustering, dimensionality reduction, reinforcement and sequence learning, scalable algorithms. Each topic is accompanied by a survey of key machine learning algorithms solving the problem and is illustrated with a set of realworld examples. The primary objective of the course is giving a broad overview of major machine learning techniques. Particular attention is paid to the modern data analysis libraries which allow solving efficiently the problems mentioned above.

Mikhail Belyayev, Maxim Panov 
3  MA03111 
Introduction to Petroleum Engineering
The course is an introduction to Petroleum Engineering and gives an overview of Petroleum Engineering and its various components and their internal connection.
The course will address the story of oil from its origin to the end user. The objective is to provide an overview of the fundamental operations in exploration, drilling, production, processing, transportation, and refining of oil and gas. As additional topics it is planned to consider Permafrost Engineering and Flow Asuurance, which are actual for Russian Oil&Gas Industry. Within the framework of the course it is planned to invite speakers form industry. 
Evgeny Chuvilin  6  MA06064 
Introduction to Scientific Computing  Maxim Fedorov  3  MA03229 
Introduction to Surface Physics  Andrey Ionov  3  MA03218 
Introduction to The Quantum Field Theory
Introduction to basic notions of gauge theory: gauge invariance, SU(N) Lie algerbras and their representations, Yang Mills Largangian and its quantization, FaddeevPopov method, ghosts and unitarity, diagram technique, basics on perturbation theory, analysis of simplest Feynman diagramms, beta function in nonabelian YangMills theory, renormalization group, asymptotic freedom, Higgs mechanism, basic notions of QCD and electroweak interaction. Depending on progress: some advanced topics: anomalies, instantons.

Yaroslav Pugai  3  MA06273 
Introduction to The Theory of Disordered Systems
This course is mainly dealing with the quantum electronic properties of disordered materials. I start with a review of different types of disorder and general methods of their theoretical treatment. Then I give a detailed discussion of the two popular models of quenched disorder, widely used for description of quantum solid state systems: Anderson model and Lifshits model. I discuss the properties of the disordered systems in the insulating phase: the density of states, the tails in the optical absorption ( with the optimal fluctuation method) and different versions of hopping conductivity: the nearest neighbour hopping and the Mott's variable range hopping. I also take into account the longrange Coulomb correlations and derive the Coulomb gap in the density of states and the EfrosShklovskii law for the conductivity.
As to the vicinity of the metalinsulator transition, I give a qualitative discussion of the mechanism behind the transition, as well as the most powerful tools for probing the properties of the system near the transition: analysis of inverse participation ratios and the concept of multifractality of the wavefunctions. In the metallic phase I discuss the weak localization corrections, including magnetoresistance, inelastic phasebreaking mechanisms and interactioninduced anomalies in the density of states near the Fermi surface. At the end of the course I give a brief introduction to mesoscopics, including the Landauer formalism and quantization of the ballistic conductance. 
Alexey Ioselevich  3  MA06274 
Lie Groups and Lie Algebras, and Their Representations
We shall begin with the basics of the theory of Lie groups and Lie algebras. Then we shall provide an accessible introduction to the theory of finitedimensional representations of classical groups on the example of the unitary groups U(N).
Tentative plan: linear Lie groups and their Lie algebras; universal enveloping algebras; Haar measure on a linear Lie group; general facts about representations of compact groups and their characters; radial part of Haar measure; Weyl's formula for characters of the unitary groups; Weyl's unitary trick; classification and realization of representations; symmetric functions. 
Grigory Olshanski  3  MA06173 
Mathematics for Data Science
This course provides substantial introduction into several mathematical disciplines that make up the foundation of mathematical methods and tools of the modern data science. Namely, probability theory and mathematical statistics, optimization theory, linear algebra, discrete mathematics, basic calculations.
Course goal is to give students basic knowledge about the main areas of mathematics used in the data science, who will continue to study their chosen more specialized areas of the modern data science. 
Grigory Kabatiansky  3  MA03112 
Modern Problems of Mathematical Physics  Andrei Marshakov  1.5  MA12268m 
Modern Problems of Theoretical Physics
The seminar "Modern Problems in Theoretical Physics" is a journal club meeting weekly to discuss a recent research paper of interest to the participants. The discussion is lead by one of the group members via a blackboard presentation. The goal of the seminar is twofold. From the one side, it assists the students in keeping track of interesting developments in the field of condensed matter physics. From the other side, it provides the group members with experience of thoughtful reading of original research papers and participation in scientific discussions, while helping them to shape their own interests.

Mikhail Feigelman, Konstantin Tikhonov 
1.5  MA12268p 
Modern Random Matrix Theory
The aim of this course is to provide an introduction to asymptotic and nonasymptotic methods for the study of random structures in high dimension that arise in probability, statistics, computer science, and mathematics.
One of the emphases is on the development of a common set of tools that have proved to be useful in a wide range of applications in different areas. Topics will include the concentration of measure, Stein’s methods, suprema of random processes and etc. Another main emphasis is on the application of these tools for the study of spectral statistics of random matrices, which are remarkable examples of random structures in high dimension and may be used as models for data, physical phenomena or within randomized computer algorithms. The topics of this course form an essential basis for work in the area of high dimensional data. Students will study how to apply the main modern probabilistic methods in practice and learn important topics from the random matrix theory. 
Alexey Naumov  3  MA03130 
Molecular Biology 1
Molecular biology 1 course is based on learning the principles of replication, recombination and DNA repair. Additionally, replication strategies of phages and viruses will be discussed. Mitosis and meiosis will be described in a context of DNA biosynthesis.
The goal of the course is obtaining a comprehensive knowledge on the structure of DNA and processes of DNA replication, recombination and repair in bacteria and eukaryotes, as well as on replication of phages and viruses. Students activities include: listening to lectures discussions/seminars homework tests 
Petr Sergiev  3  MA03220 
Molecular Biology Seminar
This seminar will cover original research papers on CRISPRCas from the period of 2003 to 2012, before the seminal advances that lead to development of genomic engineering. Each seminar will consist of in depth critical discussion of primary papers from the period given by two students in front of the rest of the class with particular attention given to research methodology and critical evaluation of the data. Papers send out to the class before the seminar to prepare for presentation/discussion.

Konstantin Severinov  3  MA03052 
Molecular Biology Seminar
This seminar will cover original research papers on CRISPRCas from the period of 2003 to 2012, before the seminal advances that lead to development of genomic engineering. Each seminar will consist of in depth critical discussion of primary papers from the period given by two students in front of the rest of the class with particular attention given to research methodology and critical evaluation of the data. Papers send out to the class before the seminar to prepare for presentation/discussion.

Konstantin Severinov  3  PA03052 
Nanooptics
Nanooptics aims at the understanding of optical phenomena on the nanometer scale, i.e. near or beyond the diffraction limit of light. Typically, elements of nanooptics are scattered across the disciplines. Nanooptics is built on the foundation of optics, quantum optics, and spectroscopy. In the presence of an inhomogeneity in space the Rayleigh limit for the confinement of light is no longer strictly valid. In principle infinite confinement of light becomes possible, at least theoretically.
The course will cover basic theoretical concepts, multiphoton microscopy, interaction of light with nanoscale systems, optical interaction between nanosystems, and resonance phenomena, namely localized surface plasmons, surface plasmon polaritons, and microresonators. 
Vladimir Drachev  3  MA03153 
Physics of Partially Disordered Systems  Pavel Dolganov  3  MA03215 
Physics of Semiconductors and Insulators  Vladimir Kulakovsky  3  MA03214 
Quantum Mechanics
The course will review the basic concepts of quantum mechanics. It is intended both for those who studied quantum mechanics previously and for those who did not. The purpose of the course is not only to introduce the main principles of quantum mechanics but to familiarize with them through active problem solving, which is the only practical way to study quantum mechanics. The course will cover the main topics such as onedimensional motion, perturbation theory, scattering theory, approximate methods in quantum mechanics, density matrix formalism.

Mikhail Skvortsov  3  MA03177 
Scientific Computing
This is an introductory course to Scientific Computing with a focus on mathematical and algorithmic aspects of HighPerformance Computing (HPC) techniques and their areas of applications. The course has also a practical component, consisting of learning basic principles of HPC and applying the acquired knowledge and skills to solving industryrelevant problems in oil & gas, electrochemical energy storage, aerospace, food and pharmaceutics.
The practical aspects of use of a variety of computational techniques for solving scientific and engineering tasks will be taught during practical demonstrations and they will be integrated as much as possible with the corresponding theoretical materials given during the lectures. During the practical demonstrations the students will get access to the parallel cluster in Skoltech. All topics in the course will be covered at an advanced introductory level, with the goal that after passing the course the students will learn enough to start using scientific computing and HPC methods in their everyday research work. Once the students reached that level, they will learn more details and more advanced subjects in other courses in the overall Computational Science & Engineering program. Students should be comfortable with undergraduate mathematics, particularly with basics of calculus, linear algebra and probability theory. Some preliminary knowledge of Unixlike operative systems is a plus. Many of the examples used in lectures and assignments will require this background. Although the course will overview most popular pieces of commercial software used in HPC, all of the software used for practical tasks in this course is open source and freely available. 
Maxim Fedorov  6  MA06113 
Statistical Physics
This is a course on rigorous results in statistical physics and random fields. Most of it will be dedicated to the theory of phase transitions, uniqueness or nonuniqueness of the lattice Gibbs fields.
The topics will include: grand canonical, canonical and microcanonical ensembles, DLR equation, Thermodynamic limit, Gibbs distributions and phase transitions, onedimensional models, correlation inequalities ( GKS, GHS, FKG), spontaneous symmetry breaking at low temperatures, uniqueness at high temperatures and in nonzero magnetic field, Nontranslationinvariant Gibbs states and interfaces, Dobrushin Uniqueness Theorem Pirogov–Sinai Theory O(N)symmetric models the Mermin–Wagner Theorem Reflection Positivity and the chessboard estimate infrared bounds 
Semen Shlosman  3  MA06180 
Stem Cells
"Stem cells" course is an introductory course aimed at providing students a broad overview of embryonic and adult stem cells and methods of reprogramming of somatic cells into induced pluripotent stem cells. Lectures and seminars of the course are focused on problems related to regulation of pluripotency and selfrenewal genes, cell signaling and signal introductions mechanisms, gene networks in various types of stem cells. The course begins from historical discoveries in the area of stem cell biology, conceptual definitions of stem cells and continues through all types of various stem cells and their features. Finial lectures consider cancer stem cells (stemness of cancer), reprogramming and regeneration.

Dmitry Papatsenko  6  MA06037 
String Theory and Conformal Theory
Conformal field theory is a quantum field theory that is invariant under conformal transformations. The course is devoted to a twodimensional theory, there is an infinitedimensional algebra of local conformal transformations.
In the course, we will discuss aspects of the conformal theory, basic, but not included in the usual introductory courses. A small preliminary acquaintance with string theory and conformal field theory is assumed. We will mainly focus on the mathematical aspects of the theory, the relations with the representation theory, geometry, combinatorics, special functions. 
Mikhail Bershtein  3  MA06260 
Strings and Cluster Varieties
The course is directed to substantive work of the master and PhD students in order to understand recently found relations among supersymmetric gauge theories, refined topological strings, cluster varieties and integrable systems. The plan of wrk on the course consists of several introductive lectures on the various consistuents of the subject as well as student talks on recent original papers and results of their own investigation. The core topics include relation between cluster varieties and Painleve equations and approaches to the SeibergWitten theories with fundamental matter based on Toda systems and spin chains.

Andrei Marshakov  1.5  MA06176 
Structural Analysis and Design
The Structural analysis and Design course gives students basics of strength analysis and design of typical structural members. Theoretical sections include stress and strain theories, failure criteria, basics of elasticity theory, nonlinear material behavior and analysis of tension, compression, bending and shear structural members. Students learn finite element software Abaqus and work on development of FE models and stress analysis of structural parts taking into account mechanical and thermal interactions.

Ivan Sergeichev  6  MA06067 
Survey of Materials
The course teaches fundamentals of modern Materials Science (Part I of the course) and provides a survey of materials (Part II), covering all relevant Skoltech research areas and beyond, with brief explanation of structural, electronic, physical, chemical or other properties of materials relevant for their practical use, or from the point of view of utilizing their unique properties in applications. It is a core course in Materials Science educational track providing a reference knowledge base for the rest of materialspecific courses as well for student research.

Andriy Zhugayevych  6  MA06063 
Theory of Phase Transitions
The role of longrange thermal fluctuations in the condensed matter
physics is considered. We give a theory of the second order transitions starting from the Landau expansion in the order parameter. As an introduction we consider the mean field theory, then we take into account fluctuations the role of which can be examined in the framework of the perturbation theory and the socalled renormgroup formalism. The peculiarities of a weak crystallization transition where fluctuations qualitatively change the nature of the phase transition in comparison with the mean field picture are treated on the same diagrammatic language. The theoretical approach based on the Landau expansion is utilized to examine thermal fluctuation effects far from phase transition points. We consider the longscale properties of smectics where fluctuations destroy the longrange order. The smectics are treated in the framework of the renormgroup approach. The same renormgroup technique is developed also for twodimensional ferromagnets where the effective coupling constant increases with increasing scale what drastically change longscale properties of the system. Longrange fluctuations are also relevant for membranes which are twodimensional objects immersed into a threedimensional fluid. Elastic modules of a membrane are logarithmically renormalized, the renormalization law can be found by using renormgroup methods. Of special interest is BerezinskiiKosterlitzThouless phase transition in superfluid, crystal or hexatic films which is related to appearing free point defects (vortices, dislocations or disclinations). The problem can be mapped into sineGordon model and then examined by renormgroup methods. We present some facts concerning critical dynamics and the socalled KPZ (KardarParisiZhang) problem. Then we consider peculiarities of the 2d hydrodynamics and passive scalar. 
Vladimir Lebedev  3  MA06138 
Topics in Neurobiology
A research paperbased course.
Overview of current research relating to various ‘hot topics’ in neurobiology and discussion of current research articles on the subject. Analysis of experiments and research described in scientific papers are presented by students and critically discussed by the class led by the instructor. Novel methods in neurobiology – optogenetics, molecular magneto technique, FLARE, transparent tissues imaging will be discussed in depth. Topics include mapping of the brain and behavior, optogenetic manipulation of memory engrams, mouse models of Alzheimer disease, synaptic plasticity, dendritic spines morphology, pathology and neurodegenerative diseases. 
Dmitry Artamonov  3  MA03104 
Course Title  Lead Instructors  ECTS credits  Course Code 

Academic Communication: Preparatory English for Phd Exam
Efficient professional communication is the key to Academic success. The course is designed for PhD students who want to maximize their academic potential by boosting their ability to write research papers, present in front of multidisciplinary audiences, participate in scholarly discussions and engage in other forms of academic communication.
The main goal of the course is to enable PhD students to produce clear, correct, concise and coherent texts acceptable for the international professional community. The course serves as a preparation for the qualification language exam, which is a prerequisite for the Thesis defense. 
Elizaveta Tikhomirova  3  PE03029 
Academic English (for GUAP Students)
Proficient communication in English is essential for a successful academic career in a multinational environment. The course provides insight into relevant aspects of text structure, grammar, vocabulary, and style building the framework of academic communication.
Students will develop essential writing and presentation skills, and get ample practice in various forms of scholarly discourse, such as writing research papers, making presentations with visual aids, and taking part in scientific discussions. 
Elizaveta Tikhomirova  3  ME03028 
Academic Writing (Theory and Practice)
The ability to use proper English for professional purposes is becoming more and more urgent nowadays. Planning, writing, revising and editing your own work in a lingua franca of modern science is one of the key skills a scientist should have. The aim of the course is to help the students plan the written work (a paper/ a thesis), understand its major parts and the language typical of them. The course will familiarize the students with major problems the Russian authors have in the English formal writing as well as the ways to overcome them. Extensive writing, self and peer editing and getting feedback from the lecturer will provide grounds for future autonomous writing.

Anastasiia Sharapkova  3  ME03027 
Advanced Optimization
The course is devoted to optimization methods and optimization problems design with a special attention to those motivated by data science, engineering and industrial applications.
The course starts with a brief reminder of the foundations of convex analysis. Then we discuss zero, first and second order methods with a special focus on their efficient implementation. We distinguish between various problem classes, discuss suitable methods for every class. The problem formulation and its proper reformulation is the critical issue for an optimizer. We’ll learn about optimization models and convex relaxations. Special attention will be addressed to Linear Matrix Inequalities (LMI) that arise in optimization problem formulations. One of the home assignments is devoted to understanding the constraints of performance for different software packages. At the last part of the course we move further to advanced first order optimization methods such as proximal mirror descent and extra gradient methods and discuss how to utilize problem structure (e.g. sparsity and separability) to speed up the methods. Within engineering and practical sections, we show how to use the methods above to crack convex and nonconvex problems arises in engineering, energy systems, machine learning and related fields. 
Elena Gryazina  6  MA06199 
Advanced PLM Techniques I: Digital Design and Optimization
This course is dedicated to the endtoend design methodology, based on the PLM approach. During the course students will develop small unmanned aerial vehicle with deployable wings.
The design includes: concept development, conceptual design, systems engineering, 3D physical simulation (CFD and FEM), parametric and topology optimization, final solid design. Educational process is focused on teamwork in this course. Siemens Teamcenter PLM platform is used as to provide interaction within students workgroup. The course provides students with a theoretical and practical basis for implementing projects devoted to the design of complex technical systems, such as unmanned aerial vehicles. 
Ighor Uzhinsky  6  MA06252 
Advanced Quantum Mechanics
Lecture Course “Advanced Quantum Mechanics” comprises a number of topics which are not included in standard courses on Quantum Mechanics. Meanwhile, these topics acquire increasing importance during last 23 decades due to developing applications in various branches of quantum condensedmatter physics theory dealing with manybody problems and problems of interaction between quantum particle and external bath.
The first set of topics refer to nontrivial examples of adiabatic or weakly nonadiabatic behavior of quantum system: Berry phases, LandauZener tunneling (including Feynman path integral representation for tunneling phenomena). Secondly, we will study nonadiabatic phenomena due to interaction between quantum particle and surrounding media, including: orthogonality catastrophe, density matrix formalism and decoherence. Third part of the course is devoted to the theory of dissipation in Quantum Mechanics 
Mikhail Feigelman, Konstantin Tikhonov 
3  MA03207 
Advanced Solid State Physics
The course presents an overview of solidstate physics with emphasis on the quantum properties of solids. It covers quantum theory of electronic and lattice degrees of freedom, magnetism and superconductivity, including, in particular, stronglycorrelated electronic systems and hightemperature superconductivity. The course also includes a review of experimental techniques used in the modern solidstate physics research.
The course assumes basic preliminary knowledge of quantum mechanics and statistical physics. Secondquantization formalism is introduced and used throughout the course. 
Boris Fine  6  MA06068 
Applied Methods of Analysis  Khoroshkin  3  ME06013 
Asymptotic Methods in Complex Analysis
In this course, students encounter a range of asymptotic methods, good for evaluation of ordinary and path integrals, solving linear and nonlinear differential equations with corresponding connection problems. Most of the techniques are motivated by examples from theoretical physics (quantum mechanics or quantum field theory). We start from formal construction of asymptotic series, proceed with resummation techniques and their applications to constructing solutions to nonlinear ODEs. Next, we discuss asymptotic matching techniques, including nonlinear connection problems. Finally, we discuss approaches to asymptotic evaluation of path integrals.

Tikhonov  3  MA06275 
Basic Molecular Biology Techniques 1
The purpose of this course is to provide students with the opportunity to obtain and develop the basic set of skills needed to be successful in a molecular biology laboratory. The course consists of handson laboratory work, as well as lectures from course instructors. Students without any significant background in the biological sciences should be advised that additional reading outside of the scheduled classes may be necessary to maximize classroom success (instructors are happy to provide resources at the students’ request).

Svetlana Dubiley  6  MA06022 
Bioinformatics Lab Course
This course is aimed for the first year master students with no prior knowledge in bioinformatics. The main course idea is to get students from different backgrounds acquainted with basic tools and algorithms in bioinformatics, such as basic phylogenetic analysis, algorithms behind sequence alignments, protein structure analysis, gene and genome annotation, as well as main databases storing sequence, protein and epigenetics data.
The knowledge obtained during this course can be immediately utilized in real biological and computational projects. 
Mikhail Gelfand  6  MA06065 
Communication Technologies for Iot
This is a newly developed course that prepares students for the applying modern telecommunication technologies, both wired and wireless in the Internet of Things area.
The course combines lectures and labs related to hardware, transmission techniques, the mediumaccess control layer, networking, applications and standards for the IoT communication technologies. All technologies are considered with usecase based approach that shows their practical application in real industrial and research scenarios. 
Dmitry Lakontsev  3  MA03234 
Computational Chemistry and Materials Modeling
The course provides an overview of modern atomistic computer simulations used to model, understand, and predict properties of realistic materials. The emphasis is on practical techniques, algorithms and programs to bridge theory and applications, from the discovery of materials to their use in realworld technologies. This introductory course is intended for both theoreticians and experimentalists in modern Materials Science at academic level ranging from MSc students to PhD students and postdocs. For more information please see the course website at http://zhugayevych.me/edu/CC/index.htm

Andriy Zhugayevych  6  MA06008 
Continuum Mechanics
Continuum mechanics is a section of mechanics and theoretical physics, or rather the continuation of theoretical mechanics that deals with analysis of deformable bodies. However, mathematics in continuum mechanics represents the main constructive tool. Continuum mechanics allows to demonstrate the power of logic and mathematical thinking. Based on a few fundamental postulates and principles, using the mathematical apparatus can reveal nontrivial, and even striking results.
Foundation of continuum mechanics consists of: This course uses tensor representations in the Cartesian coordinate system of the observer. But it will one shown in detail how to to write the continuum mechanics equations in the arbitrary curvilinear coordinate system. This way the common link is not lost and the exposition becomes easier and clearer. 
Robert Nigamatulin  6  MA06181 
Differential and Symplectic Geometry  Maxim Kazaryan, Sergei Lando 
3  MA06175 
Dynamical Systems and Ergodic Theory
Dynamical systems in our course will be presented mainly not as an independent branch of mathematics but as a very powerful tool that can be applied in geometry, topology, probability, analysis, number theory and physics. We consciously decided to sacrifice some classical chapters of ergodic theory and to introduce the most important dynamical notions and ideas in the geometric and topological context already intuitively familiar to our audience. As a compensation, we will show applications of dynamics to important problems in other mathematical disciplines. We hope to arrive at the end of the course to the most recent advances in dynamics and geometry and to present (at least informally) some of results of A. Avila, A. Eskin, M. Kontsevich, M. Mirzakhani, G. Margulis.
In accordance with this strategy, the course comprises several blocks closely related to each other. The first three of them (including very short introduction) are mainly mandatory. The decision, which of the topics listed below these three blocks would depend on the background and interests of the audience. 
Aleksandra Skripchenko, Anton Zorich 
3  MA06257 
Energy Colloquium
The Energy Colloquium educates the audience in the presentday research and applications within the broader field of Energy Science and Technology. The Colloquium consists of a series of presentations by invited academic and industry speakers. The presentations target a nonspecialist audience.
All Master and Ph.D. students within the Energy Program are encouraged to attend the Energy Colloquium during the entire period of their studies. Students can earn 1 credit, if he/she participates in the Energy Colloquium over the course of any 2 terms of the academic year. Students who passed one round can make next (for credit) over the course of their subsequent studies. 
Alexei Buchachenko  1  MA04092 
English. Candidate Examinations
This is a metacourse which allows PhD students to register for English Qualification Exam for the Russian PhD Degree. There will be no lectures or seminars, only the exam. The preparatory course is also available in course catalog (look for "Academic Communication for PhD students" course).
The Exam has two parts: Part 1 – Preexam activities (Assignments 1, 2a, 2b) 
Elizaveta Tikhomirova  3  PE03003 
Fundamentals of Photonics
This course is aimed for the first year master students, and provides an overview of the main physical principles of photonics and photonic devices. The emphasis is made on the demonstration that the light matter interaction in photonic devices can be modified by means of the modern technology. The course give the illustration how the basic physical laws help to get qualitative understanding of different branches of photonics such as light emission, transmission and detection. This introductory course is designed for both theoreticians and experimentalists.

Nikolay Gippius  6  MA06160 
Geometric Representation Theory
Geometric representation theory applies algebraic geometry to the problems of
representation theory. Some of the most famous problems of representation theory were solved on this way during the last 40 years. The list includes the Langlands reciprocity for the general linear groups over the functional fields, the LanglandsShelstad fundamental Lemma, the proof of the KazhdanLusztig conjectures; the computation of the characters of the finite groups of Lie type. We will study representations of the affine Hecke algebras using the geometry of affine Grassmannians (Satake isomorphism) and Steinberg varieties of triples (DeligneLanglands conjecture). This is a course for master students knowing the basics of algebraic geometry, sheaf theory, homology and Ktheory. 
Mikhail Finkelberg  3  MA06271 
Hamiltonian Mechanics
This is the first among the base courses in the theoretical physics, aimed for the master
students. Matematical methods of modern theory of Hamiltonian systems are based on the concepts, The preliminary program of the course includes: 
Andrei Marshakov  3  MA06174 
History and Philosophy of Science. Candidate Examinations
The aim of this course is to give to Scoltech students and postgraduates some basic information about the main stages of the development of science from its birth in Ancient Greece through the Middle Ages and the Renaissance to Modern Times and to the great scientific revolutions of the XX century. Every man of culture especially a future scientist should know the impact of such great thinkers as Plato, Aristotle, Thomas Aquinas, Jean Buridan, Nicholas of Cusa, Copernicus, Galileo, Descartes, Newton, Boscovich, Darwin, Mendel, Bohr and Einstein (omitting many other brilliant names, that would be spoken about in the frames of the course) to the development of a scientific picture of the universe. Also there will be discussed the main topics and notions of the philosophy of science: demarcation between science and humanities, Popper’s theory of falsification, Kuhn’s theory of scientific revolutions, the concept of research programmes of Lakatos and methodological anarchism of Feyerabend. We'll also discuss Lombroso's theory of genius and folly, Spengler's morthology of culture and Wittgenstein's language games.

Ivan Lupandin  6  PE06026 
Ideas to Impact: Foundations for Commercializing Technological Advances
Technological innovation is critical to the survival and competitiveness of emerging and existing organizations. This course lays the foundation to undertake a robust analysis and design of opportunities for technologybased commercialization. We introduce tools and frameworks that help isolate and control the factors shaping the identification, evaluation and development of commercial opportunities. Throughout the course we use technology examples originating from problem sets found in engineering and scientific education to develop the skills necessary to connect technology and impact.
At the same time, through creativity lab students will be introduced to a variety of creative problem solving techniques and learn how to apply these techniques in the context of the development, evaluation and application of ideas and concepts with commercial potential; consider the evaluation of business ideas that translate existing business models into new national contexts. The course is designed to help students develop the ability to find, evaluate, and develop technological ideas into commercially viable product and process concepts, and build those concepts into viable business propositions. The material covered is research and theorybased but the course is practiceoriented with much of the term spent on shaping technologybased opportunities. A central objective of this subject is to equip students with an understanding of the main issues involved in the commercialization of technological advances at both strategic and operational levels. 
Zelijko Tekic  6  MC06002 
Immunology
The purpose of this course is to lay the foundation for understanding the principles of the immune system functioning. Such a basis is necessary for further professional growth either in the field of fundamental immunology or applied research and development in medical immunology and oncology. This course will also be important for those who want to professionalize in medical practice, pharmaceutical industry, epidemiology and health services management, engineering and business in the field of biomedicine.
The course is focused on the human immune system. The main medical aspects related to the functioning of the immune system will be considered, such as: autoimmune diseases, allergies, tumorimmune system interactions, immunotherapy, vaccinations and transplantation. Particular attention will be paid to the adaptive part of the immune system and immunogenomics: application of the new sequencing technologies and associated computational data analysis approaches to the studying of the antibody and Tcell receptor repertoires in health and disease. The course is designed for students of different biomedical background. The necessary foundation will be given in the form of lectures. Independent work of students, mainly in the form of presentations aimed to dissect the particular immunological questions at the seminars, will be differentiated in compliance with individual background. A workshop in applied bioinformatics is included within the course. In a few hours of guided and independent work it will cover the data analysis of immune receptor highthroughput sequencing. 
Dmitry Chudakov  3  MA03172 
Industrial Applications of Biomedical Science
The course aims to provide students with an understanding of applications and practices of biomedical science in industrial healthcare. To put it simple, we will discuss where and how Skoltech graduates may employ their skills beyond academy science. To achieve this goal the course will decompose industry into the value chain of independent but interconnected entities and then make deep investigation of motives, profits, and costs of any segment/entity of this value chain. The incomplete list of such entities will include: R&Ddriven startups, CROs, CMOs, regulators, integrated pharmas, marketing agents, distributors, retail, hospitals, doctors. The emphasis will be made on the value chain groups that are immersed into the challendge of transforming high technologies into groundtoearth patient benefit. Such challenges will be taught through combination of business cases, class lectures, class games, and invited speakers. In terms of teaching methods, special emphasis will be made on class games that will push each course participant into active personal work, intensive sharing and receiving intensive experiences and learnings. Special emphasis of the course will be on the features and peculiarities of existing and budding Russian pharmaceutical enterprises that provide immediate employment opportunities for interested students. Course will discuss not only scientific and technological angles of the industrial drug development, but also organization and business aspects that are indispensable to any industrial work: financing, strategy, organizational structures, and project management.

Dmitry Kulish  6  MA06251 
Innovation and Intellectual Property Studies Doctoral Seminar
This course is a compulsory academic seminar series for all Ph.D. students in the Innovation and Intellectual Property Management Ph.D. Program. It consists of weekly research seminars that address the state of the art in research about the role of intellectual property in technological innovation. Specific topics and themes in the course will vary from year to year, but will typically include: theories of innovation; concepts and theories in IP management; practical issues in IP management; case studies in IP strategy; valuation of IP; Russian and international trends in intellectual property law; topics in technology entrepreneurship; product development and new technology; IP and design; patent analytics for innovation research; commercialization strategies of technology startups; organizational issues in technology innovation; conceptual issues at the interface of technology, science and business; public policy for technology, science and innovation; ethical and social issues related to IP and technological innovation; case studies in innovation management; philosophy of technology and philosophy of intellectual property; theory and methodology in IP management research; technology transfer and commercialization of university research; international collaboration and international trade in technology. As part of their seminar obligations, all students must prepare a formal written research paper on a topic that may or may not be directly related to their thesis research and make a presentation about the paper to the seminar group. The paper will be assessed.

Kelvin Willoughby  special  PC06009 
Instrumental Methods in Molecular Biology
This course is devoted to the principles of main instrumental methods that are used today in molecular biology. The aim of this course is to provide knowledge of modern methods for master students with little or no background in the field of molecular biology. A summary of modern approaches will introduce students to the general principles of methods in the biomedical research. By focusing on examples of the biomolecule purification and purity confirmation the idea of accurate studies will be explained. The course will provide a comprehensive summary of the major methods used nowadays in the field, except microsopy. Current trends will be reviewed, along with a discussion of methods application for common tasks. Some attention will be paid to minituarization of analytical devices for the use as POC (pointofcare).

Timofey Zatsepin  3  MA03250 
Integrable Systems 2
The course is devoted to quantum integrable systems. The history of quantum integrable systems starts from 1931 when
H.Bethe managed to construct exact eigenfunctions of the Hamiltonian of the Heisenberg spin chain with the help of a special substitution which became famous since that time (ansatz Bethe). In one or another form this method turns out to be applicable to many spin and fieldtheoretical integrable models. From the mathematical point of view, Bethe's method is connected to representation theory of quantum algebras (qdeformations of universal enveloping algebras and Yangians). Here is the list of topics which will be discussed in the course. – Coordinate Bethe ansatz on the example of the Heisenberg model and – Bethe ansatz in exactly solvable models of statistical mechanics – Calculation of physical quantities in integrable models in thermodynamic – Bethe equations and the YangYang function, caclulation of norms of Bethe – Quantum inverse scattering method and algebraic Bethe ansatz, quantum Rmatrices, – Functional Bethe ansatz and the method of Baxter's Qoperators, functional The knowledge of quantum mechanics and statistical physics for understanding of 
Anton Zabrodin  3  ME06010 
Introduction to Blockchain
This course provide an overview of modern blockchain technology and its' practical applications (Cryptocurrency, Certification, Anchoring. Industrial examples.) We will start from basic cryptography and distributed data base systems and show how these tools are used in blockchain. The covered topics are the following:
) Introduction to cryptography, type of ciphers. Private and Public crypto systems 
Alexey Frolov  3  MA03272 
Introduction to Solid State Physics
This course gives an introduction to solid state physics, one of the cornerstones on which a modern technologies are based. We will begin with the conventional classification of solids on the basis of binding forces, to be followed by crystal structure description and experimental techniques for crystal studies. From there we will discuss classical and quantum aspects of lattice dynamics and begin the study of the electronic structure of solids, including energy band formalism and carrier statistics in metals, semiconductors and insulators. Next we will consider basics of the atomic and electronic processes at crystal surfaces and interfaces, kinetic effects and scattering of the electrons. We will continue with the study of the optical processes in solids, including nonequilibrium carrier dynamics and photovoltaic effects and their applications in technology.

Sergey Kosolobov  6  MA06027 
Introduction to The Quantum Field Theory
Introduction to basic notions of gauge theory: gauge invariance, SU(N) Lie algerbras and their representations, Yang Mills Largangian and its quantization, FaddeevPopov method, ghosts and unitarity, diagram technique, basics on perturbation theory, analysis of simplest Feynman diagramms, beta function in nonabelian YangMills theory, renormalization group, asymptotic freedom, Higgs mechanism, basic notions of QCD and electroweak interaction. Depending on progress: some advanced topics: anomalies, instantons.

Yaroslav Pugai  3  MA06273 
Introduction to The Theory of Disordered Systems
This course is mainly dealing with the quantum electronic properties of disordered materials. I start with a review of different types of disorder and general methods of their theoretical treatment. Then I give a detailed discussion of the two popular models of quenched disorder, widely used for description of quantum solid state systems: Anderson model and Lifshits model. I discuss the properties of the disordered systems in the insulating phase: the density of states, the tails in the optical absorption ( with the optimal fluctuation method) and different versions of hopping conductivity: the nearest neighbour hopping and the Mott's variable range hopping. I also take into account the longrange Coulomb correlations and derive the Coulomb gap in the density of states and the EfrosShklovskii law for the conductivity.
As to the vicinity of the metalinsulator transition, I give a qualitative discussion of the mechanism behind the transition, as well as the most powerful tools for probing the properties of the system near the transition: analysis of inverse participation ratios and the concept of multifractality of the wavefunctions. In the metallic phase I discuss the weak localization corrections, including magnetoresistance, inelastic phasebreaking mechanisms and interactioninduced anomalies in the density of states near the Fermi surface. At the end of the course I give a brief introduction to mesoscopics, including the Landauer formalism and quantization of the ballistic conductance. 
Poselevich  3  MA06274 
Lie Groups and Lie Algebras, and Their Representations
We shall begin with the basics of the theory of Lie groups and Lie algebras. Then we shall provide an accessible introduction to the theory of finitedimensional representations of classical groups on the example of the unitary groups U(N).
Tentative plan: linear Lie groups and their Lie algebras; universal enveloping algebras; Haar measure on a linear Lie group; general facts about representations of compact groups and their characters; radial part of Haar measure; Weyl's formula for characters of the unitary groups; Weyl's unitary trick; classification and realization of representations; symmetric functions. 
Grigory Olshanski  3  MA06173 
Magnetic Phenomena At Macro, Micro and Nanoscales
Objectives of this course are as follows: the mastery of the fundamental concepts, laws and theories of physics of magnetic phenomena; introduction to basic experimental techniques to characterize magnetic materials; modern applications of magnetics. The importance of these topics results from application of thin magnetic films as the layers in heterostructures which control the operation of micro and cryolectronics devices. The straightforward scaling is impossible when one goes from the bulk magnetic materials to micro and nmsize systems because of the principle difference in dynamic behavior and appearance of new types of excitations.

Lyudmila Uspenskaya  3  MA03219 
Materials Chemistry
The goal of this course is to provide a survey of materials chemistry and their characterization techniques with an emphasis on chemical, electrical, optical and magnetic properties. Further emphasis will be placed application of materials chemistry to energy storage and conversion processes (batteries, fuel and solarcells)
Upon completion of this course the students will be able to master: 1.Classes of Materials crystalline solids ionic, covalent, metallic, polymers 2. Property of Materials Electrical 3. Materials Chemistry Analysis Methods Surface Sensitivity and Specificity 
Keith Stevenson  6  MA06042 
Mathematical Models in Biology
The course aims to teach students to quantify biological observations into conceptual models, frame these models in mathematical terms, and analyze these models, both qualitatively and numerically.
It includes considering strategies to choose the relevant variables, parameters and observables, model nature (e.g. discrete vs continuous), modeling technique (e.g. agentbased simulations vs. dynamical system approach), and visualization and interpretation of the results. The following classes of systems will be used as examples: 1. Population models 
Yaroslav Ispolatov  6  MA06033 
Mechanics and Physics of Advanced Manufacturing
This course is developed to give students a broad background and hands on experience in manufacturing of advanced composite materials. Both materials and manufacturing methods are discussed. A brief introduction to advanced composite materials and processes is presented. The course is focused on the innovative nonautoclave technologies of thermosetting resin based/fiber reinforced advanced composites. Manufacturing is covered in terms of the major steps required to fabricate laminated composite parts. These will be described and discussed in details and worked out experimentally through conducting a set of lab projects. The following technologies and methods will be covered: Vacuum Infusion, Press Molding, Pultrusion, Filament Winding, and Mechanical Testing. Typical problems of materials, tooling, cure, and technological defects will be discussed. The physics, chemistry, and mechanics to develop the fundamental and constitutive laws describing the processing steps of the polymer composite fabrication processes will be discussed.

Iskander Akhatov  6  MA06240 
Micromechanics
Micromechanics studies materials that are heterogeneous at microscale. They may be manmade (concrete, metals, composites, coatings) or naturally occurring (porous and cracked rocks, bone). Matrix composites – continuous matrices containing various inhomogeneities (pores, cracks, fibers, foreign particles) – constitute an important example. The goal of micromechanics is to relate the physical behavior of such material – in particular, their overall (effective) properties – to the microstructure (geometric arrangement of the constituents and their properties). The course focuses on two groups of effective properties: the elastic and the conductive ones. The course covers the following topics:
Background results on elasticity and thermal/electric conductivity. Quantitative characterization of microstructure. Isolated inhomogeneity problem (Eshelby problem) in the context of elasticity and thermal or electrical conductivity. Property contribution tensors for effective elastic, thermal, and electric properties. Effective properties of heterogeneous materials: Variational bounds Noninteraction approximation Differential scheme Effective field approaches Crossproperty connections. The material will be illustrated by examples from various applications – plasma sprayed coatings, composites, metal foams, bones. The lectures will be supplemented by weekly homework assignments. The students will be evaluated on the basis of two midterm exams and final exam. 
Igor Sevostianov, Sergey Abaimov 
6  MA06247 
Modern Problems of Mathematical Physics  Andrei Marshakov  1.5  MA12268m 
Modern Problems of Theoretical Physics
The seminar "Modern Problems in Theoretical Physics" is a journal club meeting weekly to discuss a recent research paper of interest to the participants. The discussion is lead by one of the group members via a blackboard presentation. The goal of the seminar is twofold. From the one side, it assists the students in keeping track of interesting developments in the field of condensed matter physics. From the other side, it provides the group members with experience of thoughtful reading of original research papers and participation in scientific discussions, while helping them to shape their own interests.

Mikhail Feigelman, Konstantin Tikhonov 
1.5  MA12268p 
Molecular Biology 2
Molecular biology 2 course is based on learning the principles description of the basic processes of RNA biosynthesis, i.e. transcription and processing, as well as protein biosynthesis, i.e. translation, maturation and transport.
The purpose of the course is to obtain a detailed knowledge On the processes of transcription, in bacteria and eukaryotes, On the regulation of transcription in bacteria and eukaryotes, On examples of complex networks of transcriptional regulation in bacteria and eukaryotes, On maturation of RNA in eukaryotes On protein biosynthesis in bacteria and eukaryotes, On the transport of protein in bacteria and eukaryotes. Students activities include: listening to lectures discussions/seminars homework tests 
Petr Sergiev  3  MA03221 
Molecular Biology Seminar
This seminar will cover original research papers on CRISPRCas from the period of 2003 to 2012, before the seminal advances that lead to development of genomic engineering. Each seminar will consist of in depth critical discussion of primary papers from the period given by two students in front of the rest of the class with particular attention given to research methodology and critical evaluation of the data. Papers send out to the class before the seminar to prepare for presentation/discussion.

Konstantin Severinov  3  MA03052 
Molecular Biology Seminar
This seminar will cover original research papers on CRISPRCas from the period of 2003 to 2012, before the seminal advances that lead to development of genomic engineering. Each seminar will consist of in depth critical discussion of primary papers from the period given by two students in front of the rest of the class with particular attention given to research methodology and critical evaluation of the data. Papers send out to the class before the seminar to prepare for presentation/discussion.

Konstantin Severinov  3  PA03052 
Numerical Linear Algebra
Numerical linear algebra forms the basis for all modern computational mathematics. It is not possible to develop new large scale algorithms and even use existing ones without knowing it.
In this course I will show, how numerical linear algebra methods and algorithms are used to solve practical problems. Matrix decompositions play the key role in numerical linear algebra. We will study different matrix decompositions in details: what are they, how to compute them efficiently and robustly, and most importantly, how they are applied to the solution of linear systems, eigenvalue problems and data analysis applications. For largescale problems iterative methods will be described. I will try to highlight recent developments when it is relevant to the current lecture. This course should serve as a basis for other IT Skoltech courses. It will also serve as a firsttime place where programming environment and infrastructure is introduced in a consistent manner. 
Ivan Oseledets  6  MA06024 
Optimization Methods
This course is an applicationoriented introduction to optimization. It will focus on modeling realworld engineering tasks as optimization problems and using stateoftheart optimization techniques to solve these problems.

Victor Lempitsky  6  MA06002 
Petroleum Geophysics
The course will provide an overview of geophysical methods of hydrocarbon (HC) exploration; including classification, applications, integration; physical properties of rocks (density, susceptibility, resistivity, and seismic wave velocities). All types of geophysical methods (gravity and magnetic methods, electrical and electromagnetic (EM) methods, seismic methods, and borehole geophysical methods) will be thoroughly reviewed from the comprehensive geophysical applications but also from the standpoint of fundamental mathematical and physical principles.

Marwan Charara  6  MA06076 
Petrophysics and Reservoir Engineering
The course includes lectures in laboratory petrophysics and formation evaluation using logging, reservoir fluids analysis based on flash calculations and differential liberation, fundamentals of reservoir engineering including overall reservoir performance: material balance equation of gas, gas condensate, volatile and black oil reservoirs and decline curve analysis. Diffusivity equation and pressure transient in oil and gas reservoirs. Single and multiphase flow in porous media. Immiscible and miscible displacement processes in porous media. Well test analysis for reservoir description.

Yury Popov, Andrey Kazak, Stanislav Ursegov 
6  MA06028 
Philosophy of Science, Technology and Innovation
This course will introduce students to the art of thinking critically and philosophically about the fundamental nature of technology, the fundamental nature of science, and the practical interplay of science and technology in the process of innovation. It will focus attention on understanding the differences between technology and science, and the direction of causality between them. Is technology really “applied science” (as is often presumed) or does science depend for its progress upon the prior development of technology? Historically, which tends to come first? The course will draw heavily upon a selection of critical literature in the modern scholarly field of the philosophy of technology, exposing students to the ideas of key thinkers who are shaping the field. The following questions will also be addressed: What is the relationship between technology and human society? Does technological change evolve autonomously along an inevitable trajectory of progress, or is it socially or politically determined? Does technology embody the culture and norms of the society in which it develops? Can technology be intrinsically “good” or intrinsically “bad,” or is technology morally neutral? Should engineers and scientists be held accountable in any way for the impact of their inventions on society and nature? Can the direction of technological change be consciously controlled by humans? What does it mean to “manage” technology? Who is responsible for dealing with the impact of new technology on society? Students will participate in a series of lectures and seminars, and study a set of scholarly readings, covering themes related to the above questions. Each student will write a paper investigating and analyzing a philosophical issue related to his or her own field of scientific or engineering research or interest.

Kelvin Willoughby  3  PE06026k 
Power Electronics
The course provides an overview of the latest achievements in power electronics. The main purpose of the course is to analyze different circuit topologies, to understand how they work and which are their benefits and limitations. The course starts with reviewing the basics in electric circuit theory, and then, it introduces different kind of semiconductor devices such as diodes, thyristors and transistors. After this, power electronics circuits are presented: rectifiers, DCDC converters and inverters. The course gives the tools to analyze any kind of power converters, and provides different examples related with microgrids and energy storage applications. It has three parts: lectures, home tasks and experimental activities in the lab. By the end of the course, the students should be able to analyze a power converter, to simulate it and to understand the possible applications.

Federico Ibanez  6  MA06198 
Practicum in Experimental Physics  Valery Ryazanov  3  MA03208 
Robotics
The lecture course introduce you to basics knowledge of methods for robot design, simulation, and control of robotic system. Topics include robot kinematics, dynamics, control, design, simulation, motion planning, and AI. The course slightly touches the research in wearable, space and telexistence robotics. The projects in robotics done by the lecturer, such as NurseSim, iFeel_IM!, FlexTorque, NAVIgoid, TeleTA will be presented. The lecture aims at student preparation and motivation to conduct projects in Robotics, Automation, Advanced manufacturing, and Intelligent Systems.

Dzmitry Tsetserukou  6  MA06050 
Selected Topics in Energy: Physical, Chemical and Geophysical Challenges
The course provides an introduction to the modern topics related to fundamentals of exploration of energy resources, energy generation, storage, conversion and use. It identifies the corresponding practical challenges to be addressed at the fundamental research level and familiarizes the students with the stateoftheart approaches, methods and techniques in use in related scientific areas. The course seeks to emphasize and maintain interdisciplinary nature of the energyrelated topics, in particular, combination of micro and macroscopic approaches of geophysics, mechanics and chemistry in hydrocarbon exploration and development, relation between the physical and chemical processes of energy generation and conversion, integration of physical, chemical and mechanical approaches to perspective materials (physical and chemical synthesis, micro and macroscopic characterization, structureproperty relations, etc.) and related theoretical methodologies. These interdisciplinary links are mostly demonstrated by horizontal knowledge exchange among the students reporting and discussing practical examples from their own research field or from modern review or research publications. Topical lectures are included for further exploration of these links. The secondary aim of the course is the development of presentation skills (oral and writing), as well as scientific peerreview experience. The seminar format chosen for most activities allows students free exchange of knowledge and ideas, broader vision of their research projects and methodologies, better assessments of their own research skills and demands for further education.

Alexei Buchachenko  2  PA06106 
Space Systems Engineering
The course introduces students to the fundamentals of systems engineering as an interdisciplinary approach and means to enable the realization of successful systems, as defined by the International Council of Systems Engineering.
The course covers the entire spectrum of lifecycle management of a system, encompassing conception, design, implementation, assemblyIntegration and Test, operations, and disposal of systems. Being a foundational course for the Space and Engineering Systems students of Skoltech, the course discusses many applications of systems engineering including some parts of space systems engineering . The course also discusses systems architecture principles. The Systems Engineering course follows the systems engineering Vmodel as an educational guideline throughout the term. Tradeoff analysis and systems architecture will be introduced as part of the course, but more detailed coverage of these topics will be provided by the adhoc Systems Architecture course already in place at Skoltech. The course includes a journal club to review academic articles and standards pertinent to systems engineering, which form a complement to weekly homework assignments and a design project that is conducted throughout the term. 
Clement Fortin, Anton Ivanov 
6  MA06023 
Statistical Physics
This is a course on rigorous results in statistical physics and random fields. Most of it will be dedicated to the theory of phase transitions, uniqueness or nonuniqueness of the lattice Gibbs fields.
The topics will include: grand canonical, canonical and microcanonical ensembles, DLR equation, Thermodynamic limit, Gibbs distributions and phase transitions, onedimensional models, correlation inequalities ( GKS, GHS, FKG), spontaneous symmetry breaking at low temperatures, uniqueness at high temperatures and in nonzero magnetic field, Nontranslationinvariant Gibbs states and interfaces, Dobrushin Uniqueness Theorem Pirogov–Sinai Theory O(N)symmetric models the Mermin–Wagner Theorem Reflection Positivity and the chessboard estimate infrared bounds 
Semen Shlosman  3  MA06180 
String Theory and Conformal Theory
Conformal field theory is a quantum field theory that is invariant under conformal transformations. The course is devoted to a twodimensional theory, there is an infinitedimensional algebra of local conformal transformations.
In the course, we will discuss aspects of the conformal theory, basic, but not included in the usual introductory courses. A small preliminary acquaintance with string theory and conformal field theory is assumed. We will mainly focus on the mathematical aspects of the theory, the relations with the representation theory, geometry, combinatorics, special functions. 
Mikhail Bershtein  3  MA06260 
Strings and Cluster Varieties
The course is directed to substantive work of the master and PhD students in order to understand recently found relations among supersymmetric gauge theories, refined topological strings, cluster varieties and integrable systems. The plan of wrk on the course consists of several introductive lectures on the various consistuents of the subject as well as student talks on recent original papers and results of their own investigation. The core topics include relation between cluster varieties and Painleve equations and approaches to the SeibergWitten theories with fundamental matter based on Toda systems and spin chains.

Andrei Marshakov  1.5  MA06176 
Technology Commercialization: Foundations for Doctoral Researchers
In knowledgebased society, more than ever before, it is imperative that inventions, scientific knowledge and technological knowledge created throughout research at universities have an impact outside university faculties and laboratories. Commercialization of research is a means to fulfill that goal. This course is designed to help PhD students to consider their research ideas and results through the lenses of opportunities that are attractive for business and investors, and to prepare them to make impact through commercial execution of those opportunities.
The course lays the foundation to undertake a robust analysis and design of opportunities for technological innovation. It helps PhD students to develop the ability to recognize, evaluate, and develop technological ideas into commercially viable product and service concepts, and build those concepts into viable business propositions. We introduce tools and frameworks to help isolate and control the factors shaping the identification, evaluation and development of commercial opportunities. During the course, students first gain practical experience in shaping technologybased opportunities (originating from problems found in engineering and scientific education) and in identifying marketbased opportunities (from social, economic and environmental contexts). Students are then challenged to employ that same commercialization framework to reflect on and examine ideas and scientific results from their own doctoral research, link these with appropriate marketbased opportunities, and identify one or more pathways to create practical impact from their ideas. The material covered is research and theorybased but the course is practiceoriented with much of the term spent on shaping technologybased opportunities. A central objective of this subject is to equip students with an understanding of the main issues involved in the commercialization of technological advances at both strategic and operational levels. 
Zelijko Tekic  6  PC06002 
Theory of Phase Transitions
The role of longrange thermal fluctuations in the condensed matter
physics is considered. We give a theory of the second order transitions starting from the Landau expansion in the order parameter. As an introduction we consider the mean field theory, then we take into account fluctuations the role of which can be examined in the framework of the perturbation theory and the socalled renormgroup formalism. The peculiarities of a weak crystallization transition where fluctuations qualitatively change the nature of the phase transition in comparison with the mean field picture are treated on the same diagrammatic language. The theoretical approach based on the Landau expansion is utilized to examine thermal fluctuation effects far from phase transition points. We consider the longscale properties of smectics where fluctuations destroy the longrange order. The smectics are treated in the framework of the renormgroup approach. The same renormgroup technique is developed also for twodimensional ferromagnets where the effective coupling constant increases with increasing scale what drastically change longscale properties of the system. Longrange fluctuations are also relevant for membranes which are twodimensional objects immersed into a threedimensional fluid. Elastic modules of a membrane are logarithmically renormalized, the renormalization law can be found by using renormgroup methods. Of special interest is BerezinskiiKosterlitzThouless phase transition in superfluid, crystal or hexatic films which is related to appearing free point defects (vortices, dislocations or disclinations). The problem can be mapped into sineGordon model and then examined by renormgroup methods. We present some facts concerning critical dynamics and the socalled KPZ (KardarParisiZhang) problem. Then we consider peculiarities of the 2d hydrodynamics and passive scalar. 
Vladimir Lebedev  3  MA06138 
Transgenic Models for Drug Discovery
The subject of the discipline are the principles of the creation of genetically modified animals and obtaining of practical skills in all phases of the production of transgenic mice.
Transgenic animals are no alternative tool for studying gene function, modeling of human diseases, creating of animalproducing recombinant proteins for agricultural and pharmaceutical industries. Last years work on the creation of such organisms was intensified due to the widespread introduction of sitespecific nucleases technology: "zinc fingers», TALEN, CRISPR / Cas9 types of nuclease. Increasingly, it can be heard about the creation of new models of diseases, the use of gene knockout for medical purposes. The course "Transgenic animals" allows students not only to get acquainted with the theory of molecular biological and embryological basis of modern approaches to the modification of the genome, but also to apply their knowledge during practical training. 
Yuri Kotelevtsev  6  MA06223 
Transport in Mesoscopic Systems
The course aims to provide introduction to a modern direction of the solidstate physics, devoted to studying charge transport (charge currents) in mesoscopic structures. Mesoscopic structures are intermediate between micro and macroscopic systems; in our context, this name refers to systems with many electron in which mechanics (in particular, quantum mechanics) of single electrons is still important. The course consists of two parts, devoted to normal (i.e., nonsuperconducting) and superconducting systems. A number of these systems form a basis for nanoelectronics devices. The course assumes participation of students interested in both experimental and theoretical aspects of mesoscopic research.

Yakov Fominov  6  MA06217 
Course Title  Lead Instructors  ECTS credits  Course Code 

Academic Communication: Preparatory English for Phd Exam
Efficient professional communication is the key to Academic success. The course is designed for PhD students who want to maximize their academic potential by boosting their ability to write research papers, present in front of multidisciplinary audiences, participate in scholarly discussions and engage in other forms of academic communication.
The main goal of the course is to enable PhD students to produce clear, correct, concise and coherent texts acceptable for the international professional community. The course serves as a preparation for the qualification language exam, which is a prerequisite for the Thesis defense. 
Elizaveta Tikhomirova  3  PE03029 
Additive Manufacturing  Iskander Akhatov  6  MA06243 
Advanced Molecular Biology Techniques 1
This projectbased course provides experience with scientific project planning and implementation in the molecular biology/biotechnology lab. Coursebased research projects are geared towards the background and experience of students.The goal of the course is to teach students good laboratory practice and rational planning of the experimental work.

Konstantin Severinov  6  MA06046 
Advanced PLM Techniques II: Digital Manufacturing and Model Validation
The main goal of the course is the familiarization with the advanced manufacturing, testing, and model validation methods.
During the course, students should develop the technology for small unmanned aerial vehicle (UAV) prototype production. The course provides students with a theoretical and practical basis for advanced manufacturing of complex systems, such as UAV and forms the final understanding of the product lifecycle management. 
Ighor Uzhinsky  6  MA06253 
Advanced Statistical Methods
This course introduces the main notions, approaches, and methods of nonparametric statistics. The main topics include smoothing and regularization, model selection and parameter tuning, structural inference, efficiency and rate efficiency, local and sieve parametric approaches. The study is mainly limited to regression and density models. The topics of this course form an essential basis for working with complex data structures using modern statistical tools.
Course structure: lectures, seminars, exam. 
Vladimir Spokoiny  1.5  MA03132 
Basic Molecular Biology Techniques 1
The purpose of this course is to provide students with the opportunity to obtain and develop the basic set of skills needed to be successful in a molecular biology laboratory. The course consists of handson laboratory work, as well as lectures from course instructors. Students without any significant background in the biological sciences should be advised that additional reading outside of the scheduled classes may be necessary to maximize classroom success (instructors are happy to provide resources at the students’ request).

Svetlana Dubiley  6  MA06022 
Biostatistics
This introductory course to statistics and probability theory is modeled as an extension of a traditional university Statistics course and Advanced Placement Course in Statistics to a broader spectrum of topics, while keeping the spirit of quantitative discourse applied to reallife problems. The material is offered in 5 consecutive modules (see Course Outline below), each containing a lecture, a discussion section, and a practicum. For practical exercises we use R programming language and RStudio software. However, this course is focused on statistics rather than R; therefore, each practicum is designed with the purpose to demonstrate and reinforce understanding of concepts introduced in the lecture rather than to provide a training in R.

Dmitry Pervouchine  6  MA06036 
Computational Science and Engineering I: Modelling and Simulation
Many complex systems developed by engineers (e.g. labs on chips, iPads, magnetic resonance imaging scanners, nationwide electrical/gas/oil transportation networks, or buildings/automotive/aircraft frames or supply chains and economical/social networks) or found in nature (e.g. the human cardiovascular system, the brain neural network, biological systems, or the geophysical network of oil/water/gas reservoirs) can be viewed as large collections of interconnected dynamical system components. The performance and characteristics of each individual component critically depends on what engineers or scientists refer to as second order effects, and can be captured only by resorting to expensive partial differential equation solvers. In this course we will survey several techniques for modeling and simulation of a large variety of engineering and physical complex systems. In particular, detailed examples will be presented, drawn from the following engineering disciplines: Electrical Engineering (interconnect networks including parasitics; electromagnetic structures; analog and digital circuits including nonlinear semiconductor devices and MicroElectroMechanical Devices), Mechanical Engineering (frame modeling, heat diffusion, fluiddynamics and oil transport), Civil Engineering (structural problems, vibrations), Material Sciences (inverse problems for identification of material properties), Biomedical Engineering (human cardiovascular system).
This course provides students access to the state of the art in numerical tools in order to help them with their research projects involving analysis, design and optimization problems in a variety of different engineering and science disciplines dealing with complex systems. The focus of the course will not be on mathematical formalism and rigorous theorem proving, but rather on developing general intuition and practical implementation skills. 
6  MA06224  
Developmental Biology  Dmitry Papatsenko  6  MA06049 
Differential Topology  Alexander Gaifulin  3  MA06258 
Digital Signal Processing
Digital signal processing (DSP) refers to various techniques for improving the accuracy and reliability of digital communications. The goal, for students of this course, will be to learn the fundamentals of Digital Signal Processing from the ground up. Starting from the basic definition of a discretetime signal, we will work our way through Fourier analysis, filter design, sampling, signal statistics estimation theory, interpolation and quantization to build a DSP toolset complete enough to analyze a practical communication system in detail. We will also deal with modulation, synchronization and propagation channel modes. Handson examples and demonstration will be routinely used to close the gap between theory and practice.
The extra topics covered in this course are: – Fundamentals of random signal theory and analysis; – Modeling communication signals as random processes; – Baseband signal processing, signal synthesis and filter design for communication; – Statistical signal processing in communication; It is hoped that through learning this course students will be equipped with a clear picture of DSP as well as a necessary foundation for further study of advanced DSP topics in the future. 
Andrey Ivanov  6  MA06255 
Dynamic Systems and Control
The course focuses on dynamic systems, and their control. Such systems evolve with time and have inputs, disturbance, and outputs. One can find examples of dynamic systems in everyday life, for examples, automobiles, aircrafts, cranes, electrical circuits, fluid flow.
You will analyze the response of these systems to input. Students will learn how to control system through feedback to ensure desirable dynamic properties (performance, stability). The practice will include work with an industrial, a humanoid, a mobile, and a telepresence robot. 
Dzmitry Tsetserukou  6  MA06083 
Energy Colloquium
The Energy Colloquium educates the audience in the presentday research and applications within the broader field of Energy Science and Technology. The Colloquium consists of a series of presentations by invited academic and industry speakers. The presentations target a nonspecialist audience.
All Master and Ph.D. students within the Energy Program are encouraged to attend the Energy Colloquium during the entire period of their studies. Students can earn 1 credit, if he/she participates in the Energy Colloquium over the course of any 2 terms of the academic year. Students who passed one round can make next (for credit) over the course of their subsequent studies. 
Alexei Buchachenko  1  MA04092 
English. Candidate Examinations
This is a metacourse which allows PhD students to register for English Qualification Exam for the Russian PhD Degree. There will be no lectures or seminars, only the exam. The preparatory course is also available in course catalog (look for "Academic Communication for PhD students" course).
The Exam has two parts: Part 1 – Preexam activities (Assignments 1, 2a, 2b) 
Elizaveta Tikhomirova  3  PE03003 
Evolutionary, Population and Medical Genomics  Georgii Bazykin  6  MA06222 
Fiber Optics
The course is aimed at equipping the students with the basic understanding and typical applications of optical fibers including optical fiber communication. The course provides knowledge of optical fiber waveguide at fundamental level, essentials of an optical fiber communication system and understanding of various components of an optical fiber telecommunication system. The course starts from basics and does not require special prerequisites exceeding the standard courses of electro dynamics and quantum mechanics. The latter is necessary for understanding of the optical fiber amplifiers, which (as like as any types of optical amplifiers) cannot be described in the frame of classical approach.
The course starts from the basics of the theory of waveguides and light propagation in CW (continuous wave) and pulsed operation mode. The linear phenomena (losses, dispersion, scattering etc.) and their manifestations will be followed by several examples of nonlinear effects, typical for optical fibers – self and cross phase modulation, four wave mixing, Brillouin and Raman spontaneous scattering etc. Nonlinear solitary wave propagation (soliton pulses) will be considered as well. The next part of this course deals with the optical fiber amplifiers, namely Erbium Doped Fiber Amplifier (EDFA) and Raman Fiber Amplifier (RFA) which play crucial role in the modern fiber optic communication systems. Several fiber based devices will be described, among of them Fiber Bragg Gratings, Fiber Long Period Gratings, Fiber Couplers and Wavelength Division Multiplexors (WDM), Polarization Multiplexors (PM), Delay Lines (MachZander interferometers), and several types of fiber lasers. Finally, other noncommunication fiber types and applications will be considered including Photonic Crystal Fibers, Crystal Fibers, fibers with metallic coatings, and plastic fibers. 
Arkady Shipulin  3  MA03155 
Fracture Mechanics  Igor Sevostianov, Sergey Abaimov 
6  MA06248 
Functional Methods in The Theory of Disordered Systems
The course provides an extensive overview of contemporary functional methods in the theory of disordered systems. Starting from the theory of random matrices, it covers various aspects of electron motion in disordered media. The concept of the nonlinear supersymmetric sigma model is introduced and used as a unique language to describe such phenomena as energy level statistics, weak localization, renormalization group analysis, nonperturbative solution of the localization problem in quantum wires, electronelectron interaction, nonequilibrium phenomena in quantum dots.

Mikhail Skvortsov  3  MA06262 
Gauge Theory and Gravitation
The present course could be also entitled 'Classical Field Theory', which menas it deals with all basic material needed in a study of fields preceeding to a study of their quantum properties. This requires in particular understanding such tools as Lagrangian, action functional, field equations (EulerLagrange equations). We shall also learn what are the most important symmetry principles which put certain constraints on a field theory. With this are related conservation laws. Typical important symmetries to mention are Lorentz and Poincare symmetry, conformal symmetry, gauge symmetry, general coordinate covariance.
A traditional approach to Classical Field Theory has a perfect base in the 2nd volume of LandauLifshitz' course. However, since that prominent book was written, new elements came forward, which required more knowledge of differential geometry and topology. In our lecture course, we shall get familiar with most important basic facts from these branches of mathematics with application to field theory. For example, understanding instantons (even at a classical level) requires good knowledge of a number of notions from modern math courses, such as vector bundles, connections, homotopy groups. Therefore our course has to go beyond the reach of LandauLifshitz' volume 2. 
Alexey Rosly  3  MA06178 
Geomechanics and Hydraulic Fracturing  Artem Myasnikov, Andrei Osiptsov, Alexey Cheremisin 
6  MA06190 
Information and Coding Theory
The aim of the course is to explain basic ideas and results of information and coding theory, some of which has been used for rather long time in data science, in particular various entropy inequalities, and some emerged just very recently, for instance, usage of errorcorrecting codes for improvements of kmeans method for clustering. The course is divided into two parts: introduction to information theory and elements of modern coding theory. In the first part, we consider the measure of information, mutual information, entropy, evaluation of channel capacity for single user and multiuser channels. In the second part, we consider foundations of coding theory such as block codes, linear codes, bounds on the code’s parameters and the most popular algebraic coding methods (Hamming, ReedMuller, BCH and ReedSolomon codes). Then we consider modern coding techniques, i.e. iterative decoding systems and graphical models to represent them. Iterative techniques have revolutionized the theory and practice of coding and have been applied in numerous communications standards. We discuss lowdensity paritycheck (LDPC) codes, factor graphs and SumProduct decoding algorithm.

Alexey Frolov  6  MA06122 
Innovation and Intellectual Property Studies Doctoral Seminar
This course is a compulsory academic seminar series for all Ph.D. students in the Innovation and Intellectual Property Management Ph.D. Program. It consists of weekly research seminars that address the state of the art in research about the role of intellectual property in technological innovation. Specific topics and themes in the course will vary from year to year, but will typically include: theories of innovation; concepts and theories in IP management; practical issues in IP management; case studies in IP strategy; valuation of IP; Russian and international trends in intellectual property law; topics in technology entrepreneurship; product development and new technology; IP and design; patent analytics for innovation research; commercialization strategies of technology startups; organizational issues in technology innovation; conceptual issues at the interface of technology, science and business; public policy for technology, science and innovation; ethical and social issues related to IP and technological innovation; case studies in innovation management; philosophy of technology and philosophy of intellectual property; theory and methodology in IP management research; technology transfer and commercialization of university research; international collaboration and international trade in technology. As part of their seminar obligations, all students must prepare a formal written research paper on a topic that may or may not be directly related to their thesis research and make a presentation about the paper to the seminar group. The paper will be assessed.

Kelvin Willoughby  special  PC06009 
Integrable Systems 1  Igor Krichever, Anton Zabrodin 
3  MA06179 
Intellectual Property and Technological Innovation
Intellectual property (IP) is a critically important aspect of technological innovation and a key factor in the management of technologyintensive enterprises. Prowess in the management of intellectual property is important for technology leaders in both established corporations and entrepreneurial ventures.
Entrepreneurial technology ventures flourish according to how well their intellectual property assets are managed, leveraged and enforced. Additionally, it is almost impossible for engineers or scientists to avoid confronting issues related to intellectual property. These include: the risk of violating the IP rights of others; an obligation to respect the IP policies of one’s employer; the need to obtain IP protection for one’s own inventions and creative works; the obligation to become involved in the management of the IP belonging to ones employer; and the challenge of ensuring that one’s own IP rights are not infringed by others, including by one’s own employer or one’s clients. In addition, with such a large amount of contemporary business—in both the private sector and government—involving outsourcing and interorganizational collaboration, expertise in the licensing of intellectual property rights is in high demand. This course will survey basic concepts of intellectual property and provide an introduction to a variety of types of intellectual property and IPrelated rights, such as patents, copyright, trade secrets, trade marks, design rights, database rights, domain names, and demarcations of origin. The will also examine the strategic management of IP in the process of technology commercialization, and the resolution of IPrelated conflicts between technology based enterprises. It will also explore social, economic and ethical issues associated with the accumulation and exploitation of intellectual property. 
Kelvin Willoughby  6  MC06006 
Intellectual Property, Technological Innovation and Academic Research  Kelvin Willoughby  6  PC06006 
Introduction to Iot
In the last decade the Internet of Things (IoT) paradigm has slowly but steadily and increasingly permeated what researchers and engineers study and build. The term “Internet of Things” doesn’t have a single definition and people today often use it to interchangeably refer to Wireless Sensor Network (WSN), MachinetoMachine (M2M), Web of Things (WoT) and other concepts. The focus of this course is to learn about these technologies that will be extending the Internet as we know it and use it today, to interconnect not only people and computers but also sensors and associated objects. The course will be divided into two strongly coupled parts. The first part of the course covers the IoT ‘pillar’ technologies, i.e. embedded systems, wireless sensor networks, semantic technologies, and theory behind them while the second part will have a special focus on IoT development, i.e. IoT apps, open platforms, sensors and actuators, software/middleware. Apart from covering the theory behind the IoT and “how to connect things to the Internet”, the course will therefore also engage the students to demonstrate the feasibility of simple IoT real applications and will challenge them to improve their applications through the use of cognitive technologies and cloud computing.

Andrey Somov  3  MA03233 
Introduction to Power Systems
This course covers power systems analysis & operations, including fundamentals (balanced threephase power) steadystate analysis (power flow), state estimation, operation (optimal power flow), security (contingency analysis and security constrained optimal power flow), power system dynamics (frequency and voltage control) and challenges and trend of future power systems. After successfully completing this course, the student will be capable of analyzing the technical and economic operation of an electric energy system.

David Pozo  6  MA06007 
Laser Physics  Sergei Vergeles  6  MA06143 
Machine Learning
The course is a general introduction to machine learning (ML) and its applications. It covers fundamental modern topics in ML, and describes the most important theoretical basis and tools necessary to investigate properties of algorithms and justify their usage. It also provides important aspects of the algorithms’ applications, illustrated using realworld problems. The course starts with an overview of canonical ML applications and problems, learning scenarios, etc. and introduction into theoretical foundations of ML. We present the most novel theoretical tools and concepts trying to be as succinct as possible. Then we discuss in depth fundamental ML algorithms for classification, regression, boosting, etc., their properties as well as their practical applications. The last part of the course is devoted to advanced ML topics such that metric learning, kernel mean embedding of distributions, anomaly detection, reinforcement learning, etc. Within practical sections, we show how to use the methods above to crack various realworld problems. Home assignments include application of existing algorithms to solve applied industrial problems, development of modifications of ML algorithms, as well as some theoretical exercises. The students are assumed to be familiar with basic concepts in linear algebra, probability and real analysis.

Evgeny Burnaev  6  MA06018 
Material Structure Characterization Methods
The course teaches theoretical and practical fundamentals of diffraction and electron microscopy methods applied to the analysis of the crystal structure, nano and microstructure of materials. The course delivers basic knowledge on the theory of crystal structure analysis with various kinds of radiation, modern techniques of crystal structure determination, the analysis of the local structure of matter, defects and microstructure, theory of image formation in the electron microscope and a review on modern spectroscopic techniques with atomic resolution. The competences acquired in this course can be further used in all branches of material science dealing with crystalline matter. The course consists of lectures, seminars/practical lessons, laboratory works and exam.

Artem Abakumov  6  MA06116 
Materials and Devices for Nano and Optoelectronics  Valery Ryazanov  3  MA06206 
Mathematical and Programming Support of Software Packages and Computer Networks  Stamatios Lefkimmiatis  6  PA06121 
Modern Problems of Mathematical Physics  Andrei Marshakov  1.5  MA12268m 
Modern Problems of Theoretical Physics
The seminar "Modern Problems in Theoretical Physics" is a journal club meeting weekly to discuss a recent research paper of interest to the participants. The discussion is lead by one of the group members via a blackboard presentation. The goal of the seminar is twofold. From the one side, it assists the students in keeping track of interesting developments in the field of condensed matter physics. From the other side, it provides the group members with experience of thoughtful reading of original research papers and participation in scientific discussions, while helping them to shape their own interests.

Mikhail Feigelman, Konstantin Tikhonov 
1.5  MA12268p 
Molecular Biology Seminar
This seminar will cover original research papers on CRISPRCas from the period of 2003 to 2012, before the seminal advances that lead to development of genomic engineering. Each seminar will consist of in depth critical discussion of primary papers from the period given by two students in front of the rest of the class with particular attention given to research methodology and critical evaluation of the data. Papers send out to the class before the seminar to prepare for presentation/discussion.

Konstantin Severinov  3  MA03052 
Molecular Biology Seminar
This seminar will cover original research papers on CRISPRCas from the period of 2003 to 2012, before the seminal advances that lead to development of genomic engineering. Each seminar will consist of in depth critical discussion of primary papers from the period given by two students in front of the rest of the class with particular attention given to research methodology and critical evaluation of the data. Papers send out to the class before the seminar to prepare for presentation/discussion.

Konstantin Severinov  3  PA03052 
Neuroscience
The course is aimed for students who are new to the field of neuroscience. We outline the basic concepts and processes of brain function ranging from molecular to cognitive neuroscience. The course aims to teach students to understand the structure and function of neuronal communication in physiology and pathology at the molecular, cellular and system levels. They will learn about brainrelated diseases and pharmacology of central nervous system disorders such as ADHD, addiction, schizophrenia, bipolar disorder and Parkinson’s disease. We will also introduce common methods to study brain function. Particularly, we will introduce electrophysiological, optogenetic, imaging, voltammetric and microdialysis techniques for the study of brain function. A high emphasis will be placed on critical discussions of most uptodate methodology.

Raul Gainetdinov  6  MA06047 
NonEquilibrium Processes in Energy Conversion  Henni Querdane  6  MA06200 
Numerical Methods in Engineering and Science
Engineering science and technology are undergoing a revolution. With continuous rapid advances in hardware and software information technology, computer simulations have emerged as a new way of scientific discovery enabling scientists and engineers to build and test models of multiscale/multiphysics phenomena that are either too complex, costly, hazardous, vast, small, or even impossible for direct experimentation. In industry, computer modeling and simulations provide a competitive edge by transforming business and engineering practices. Increasingly, computer simulations are replacing physical tests to ensure product reliability and quality, while noticeably shortening design cycle.
The course is intended to provide the understanding and working knowledge of numerical methods required for modeling and simulation of complex phenomena. The course focuses on understanding fundamentals of numerical methods such as accuracy, stability, convergence, and consistency rather than learning how to use canned computer codes. The course involves a fair amount of firsthand experience with programing and solving real problems on computers. Although the solid knowledge of calculus, linear algebra, complex variables is essential, only basic understanding of the theory of ordinary and partial differential equations as governing equations for physical and engineering systems as well as basic programming skills are required. The following topics are discussed: interpolation, numerical differentiation, numerical integration, numerical solutions of ordinary differential equations, and numerical solution of partial differential equations. Students will have to complete four computer projects, midterm and final exams. 
Oleg Vasilyev  6  MA06239 
OneDimensional Quantum Systems  Lashkevich  3  MA06276 
Organic Materials for Electronics, Photonics, Energy Generation and Storage
The course provides an overview of the latest achievements in the field of material design for electronics, energy conversion and storage.
The main purpose of the course is studying the basic chemical, physical and physicochemical, e.g. surface and structural, aspects of designing novel materials with the desired properties. This course will be focused mainly on organic and hybrid materials as well as on different types of electronic devices made thereof: fieldeffect transistors and electronic circuits, sensors, memory elements, light emitting diodes, solar cells, photodetectors, lithium and sodium batteries. Using a set of examples it will be shown how the discovery of novel materials results in the development of novel technologies, innovative products and, in some cases, even leads to revolutionary changes in specific fields of science and technology. This course is designed for MS students planning to perform experimental studies in the interdisciplinary fields at the boarder of physics and chemistry with the aim of solving relevant challenges of modern materials science. 
Pavel Troshin  6  MA06119 
Pedagogy of Higher Education
The course offers an introduction to facilitating learning in higher education for PhD students who are asked to act as teaching assistants or supervisors. The course content focuses on aligning learning outcomes with learning activities and assessment strategies. Constructive alignment in the course is defined at high resolution such that learning outcomes for a course are elaborated into separate activities and assignments for students. In other words, learning outcomes need to be articulated at every level of learning activities from course to assignment.
The course also rests on the approach that learning is promoted by feedback. The assessment design that participants in the course design will therefore be required to reflect significant and effective use of continuous formative assessment. Such formative assessment requires strategic learning activities and assignments, and the course therefore comes with an emphasis on communicationtolearn activities including peer learning. Skoltech is an English medium instruction environment, and the course contains discussion topics to highlight ways of addressing the potential effects of language and culture barriers for high quality student learning. All topics in the course are applied by participants on their own teaching and learning experiences and are meant to be used as they prepare and plan for their teaching assistantships or their supervisory activities to come. All participants will have a task to produce a reflection on their future actions to evolve as facilitators and meet the requirements of the scholarship of teaching and learning. 
Magnus Gustaffson  3  PE03025 
Philosophy of Science, Technology and Innovation
This course will introduce students to the art of thinking critically and philosophically about the fundamental nature of technology, the fundamental nature of science, and the practical interplay of science and technology in the process of innovation. It will focus attention on understanding the differences between technology and science, and the direction of causality between them. Is technology really “applied science” (as is often presumed) or does science depend for its progress upon the prior development of technology? Historically, which tends to come first? The course will draw heavily upon a selection of critical literature in the modern scholarly field of the philosophy of technology, exposing students to the ideas of key thinkers who are shaping the field. The following questions will also be addressed: What is the relationship between technology and human society? Does technological change evolve autonomously along an inevitable trajectory of progress, or is it socially or politically determined? Does technology embody the culture and norms of the society in which it develops? Can technology be intrinsically “good” or intrinsically “bad,” or is technology morally neutral? Should engineers and scientists be held accountable in any way for the impact of their inventions on society and nature? Can the direction of technological change be consciously controlled by humans? What does it mean to “manage” technology? Who is responsible for dealing with the impact of new technology on society? Students will participate in a series of lectures and seminars, and study a set of scholarly readings, covering themes related to the above questions. Each student will write a paper investigating and analyzing a philosophical issue related to his or her own field of scientific or engineering research or interest.

Kelvin Willoughby  3  PE06026k 
Practicum in Experimental Physics  Valery Ryazanov  3  MA03208 
Quantum Field Theory  Vladimir Losyakov  3  ME06011 
Quantum Mechanics  Semenov  3  MA06177 
Quantum Mesoscopics. Quantum Hall Effect  Igor Burmistrov  3  MA06278 
Random Processes  TBD  3  ME06014 
Selected Topics in Energy: Physical, Chemical and Geophysical Challenges
The course provides an introduction to the modern topics related to fundamentals of exploration of energy resources, energy generation, storage, conversion and use. It identifies the corresponding practical challenges to be addressed at the fundamental research level and familiarizes the students with the stateoftheart approaches, methods and techniques in use in related scientific areas. The course seeks to emphasize and maintain interdisciplinary nature of the energyrelated topics, in particular, combination of micro and macroscopic approaches of geophysics, mechanics and chemistry in hydrocarbon exploration and development, relation between the physical and chemical processes of energy generation and conversion, integration of physical, chemical and mechanical approaches to perspective materials (physical and chemical synthesis, micro and macroscopic characterization, structureproperty relations, etc.) and related theoretical methodologies. These interdisciplinary links are mostly demonstrated by horizontal knowledge exchange among the students reporting and discussing practical examples from their own research field or from modern review or research publications. Topical lectures are included for further exploration of these links. The secondary aim of the course is the development of presentation skills (oral and writing), as well as scientific peerreview experience. The seminar format chosen for most activities allows students free exchange of knowledge and ideas, broader vision of their research projects and methodologies, better assessments of their own research skills and demands for further education.

Alexei Buchachenko  2  PA06106 
Signal and Image Processing
Nowadays, digital signals and images can be found everywhere, in a plethora of scientific (e.g., astronomical, biomedical) and consumer applications (e.g., computational photography). Therefore, the ability to analyze and process digital signals and images is an extremely important skill for engineering/science master students to obtain. Indeed, digital signal and image processing is mainly responsible for the multimedia technology revolution that we are experiencing today. Important tasks that signal and image processing techniques can successfully tackle are inverse problems, such as image enhancement and restoration, which involve the removal of degradations that signals and images suffer during acquisition (e.g. removing the blur from the digital picture of a moving object, or removing the noise from a picture taken under low light conditions).
This course will cover the fundamentals of signal and image processing. We will provide a mathematical framework to describe and analyze images as two or threedimensional signals in the spatial and frequency domains. The students will become familiar with the theory behind fundamental processing tasks including image enhancement, recovery and reconstruction. They will also learn how to perform these key processing tasks in practice using current stateoftheart techniques and computational tools. A wide variety of such tools will be introduced including largescale optimization algorithms and statistical methods. Emphasis will also be given on sparsity, which plays a central role in modern image processing systems 
Stamatios Lefkimmiatis  6  MA06121 
Spacecraft and Mission Design
This course introduces students to satellite engineering and provides theoretical fundamentals required for the design of a space mission. The course will teach design fundamentals of satellite subsystems, including payload, thermal, structures and configuration, communications, avionics, power, propulsion, ADCS, orbits, and ground systems. The theory is applied to a group design project of a space mission for novel terrestrial applications or space science purposes. After successful completion of this class, students will have acquired the body of knowledge required to design a space mission at the Preliminary Design Review (PDR) level.

Anton Ivanov  6  MA06074 
Spectroscopy of Quantum Materials  Yurii Lozovik  3  MA03162 
Strings and Cluster Varieties
The course is directed to substantive work of the master and PhD students in order to understand recently found relations among supersymmetric gauge theories, refined topological strings, cluster varieties and integrable systems. The plan of wrk on the course consists of several introductive lectures on the various consistuents of the subject as well as student talks on recent original papers and results of their own investigation. The core topics include relation between cluster varieties and Painleve equations and approaches to the SeibergWitten theories with fundamental matter based on Toda systems and spin chains.

Andrei Marshakov  1.5  MA06176 
Structure and Properties of Materials
This course is an introductory subject in the field of materials science and crystallography. The goal is to introduce students to basic concepts of structureproperty relations for materials at the microscopic level.

Artem R. Oganov  6  MA06075 
Thinking Disruptive for Big Future
The goal is to open the mind of the audience showing that there is not only one predetermined path for a career after the studies, that the world is big, fantastic and that the problems we face are huge, but fascinating. The goal is also to show that there is no, or should not be any Chinese Wall between mathematicians, physicists and engineers. Finally, the goal is to show how some ideas, some of them being very theoretical and some others not, can bring to the creation of startups. It will rely on the more than 30 years of experience of JeanFrancois Geneste who will exemplify with encountered concrete examples he met along his career. We shall go through "the law of the mean", disruptive systems (airships, pseudosatellites, launchers, mining in space, fractionation and responsive space), disruptive equipment (infinite impulse propulsion, CVC jet engine, thermal solar arrays), systems intrinsically resistant to terrorist attacks, Disruptive science (some contradictions of physics, coherent alternative, new potential sources of energy, high temperature superconductivity with a new model of the atom, communications quicker than light, analog quantum computers, infinite power quantum computers, disruptive cosmology)

JeanFrancois Geneste  6  MC06010 
Unconventional Hydrocarbons: Exploration and Development  Mikhail Spasennykh  6  MA06189 
Vertex Operator Algebras
Infinitedimensional Lie algebras (such as Virasoro algebra or affine KacMoody algebras) turn out to be very important in various areas of modern mathematics and mathematical physics. In particular, they are very useful in the description of some field theories. In this context one arranges infinite number of the Lie algebra elements into a single object called field. This idea generalizes to the general theory of vertex operator algebras. VOAs capture the main properties of the infinite diemensional Lie algebras and have rich additional structure. Vertex operator algebras proved to be very useful in many situations; the classical example is the KP integrable hierarchy. They are also extensively used in modern algebraic geometry. Our goal is to give an introduction to the theory of vertex operator algebras from the modern
mathematical point of view. We describe the main definitions, constructions and applications of the theory. The course is aimed at PhD students and master students. 
Evgeny Feigin  3  MA06259 
Course Title  Lead Instructors  ECTS credits  Course Code 

Academic Communication: Preparatory English for Phd Exam
Efficient professional communication is the key to Academic success. The course is designed for PhD students who want to maximize their academic potential by boosting their ability to write research papers, present in front of multidisciplinary audiences, participate in scholarly discussions and engage in other forms of academic communication.
The main goal of the course is to enable PhD students to produce clear, correct, concise and coherent texts acceptable for the international professional community. The course serves as a preparation for the qualification language exam, which is a prerequisite for the Thesis defense. 
Elizaveta Tikhomirova  3  PE03029 
Advanced Bioinformatics Lab
The course will introduce students to the handson practical analysis of novel biological “omics” data with a specific focus on the stateoftheart analysis of the proteome, metabolome and lipidome. The course will integrate various types of omics data generated by mass spectrometry based approaches, as well as axillary data new generation sequencing technologies.
The course will include the following parts: general principles of proteomics analysis, semiquantitative and quantitative proteomics, posttranslational modifications analysis and proteome database assembly in the proteomics section; general principles of metabolomics/lipidomics analysis, metabolite/lipid detection, quantification and annotation, metabolome/lipidome pathway analysis, systemslevel analysis in the metabolomics and lipidomics sections. The course will include practical data analysis work conducted by student in front of computer, but also introductory lectures into principles of mass spectrometry based data analysis, proteome, metabolome and lipidome organization, as well as current tools available for data analysis in these fields. At the end of the course, students would be expected to accomplish an independent data analysis project on a model dataset including several heterogeneous types of biological “omics” data. 
Philipp Khaitovich  6  MA06080 
Advanced Molecular Biology Techniques 1
This projectbased course provides experience with scientific project planning and implementation in the molecular biology/biotechnology lab. Coursebased research projects are geared towards the background and experience of students.The goal of the course is to teach students good laboratory practice and rational planning of the experimental work.

Konstantin Severinov  6  MA06046 
Advanced Statistical Methods
This course introduces the main notions, approaches, and methods of nonparametric statistics. The main topics include smoothing and regularization, model selection and parameter tuning, structural inference, efficiency and rate efficiency, local and sieve parametric approaches. The study is mainly limited to regression and density models. The topics of this course form an essential basis for working with complex data structures using modern statistical tools.
Course structure: lectures, seminars, exam. 
Vladimir Spokoiny  1.5  MA03132 
Basic Molecular Biology Techniques 1
The purpose of this course is to provide students with the opportunity to obtain and develop the basic set of skills needed to be successful in a molecular biology laboratory. The course consists of handson laboratory work, as well as lectures from course instructors. Students without any significant background in the biological sciences should be advised that additional reading outside of the scheduled classes may be necessary to maximize classroom success (instructors are happy to provide resources at the students’ request).

Konstantin Severinov  6  MA06022 
Bayesian Methods of Machine Learning
The course addresses Bayesian methods for solving various machine learning and data analysis problems (classification, regression, dimension reduction, topic modeling, etc.). The course starts with an overview of canonical machine learning (ML) applications and problems, learning scenarios, etc. and then introduces foundations of Bayesian approach to solve these problems. Bayesian approach allows one to take into account subject domain knowledge and/or user’s preferences through a prior distribution when constructing the model. Besides, it offers an efficient framework for model selection. First we discuss which prior distributions types are usually used, limit properties of a posterior distribution, and provide some illustrations of the Bayesian approach. The practical applicability of Bayesian methods in the last 20 years has been greatly enhanced through the development of a range of approximate inference algorithms such as variational Bayes and expectation propagation, as well as posterior simulation methods based on the Markov chain Monte Carlo approach. As a result Bayesian methods have grown from a specialist niche to become mainstream. Therefore, we devoted a second part of the course to approximation tools, vitally important for Bayesian inference, and provide examples how to use Bayesian approaches to automatically select features, tune the regularization parameter in regression and classification, etc. For each problem, we introduce suitable Bayesian models and show how they are used to implement inference in the given data analysis problem. The last part of the course is devoted to Bayesian nonparametric models and methods, which have become widespread in the last 20 years. We discuss theoretical nonparametric Bayesian framework and then illustrate its application using the problems of clustering with unknown number of clusters, estimation of a latent subspace dimension, Gaussian process regression, etc.

Evgeny Burnaev  6  PA06129 
Bayesian Methods of Machine Learning
The course addresses Bayesian methods for solving various machine learning and data analysis problems (classification, regression, dimension reduction, topic modeling, etc.). The course starts with an overview of canonical machine learning (ML) applications and problems, learning scenarios, etc. and then introduces foundations of Bayesian approach to solve these problems. Bayesian approach allows one to take into account subject domain knowledge and/or user’s preferences through a prior distribution when constructing the model. Besides, it offers an efficient framework for model selection. First we discuss which prior distributions types are usually used, limit properties of a posterior distribution, and provide some illustrations of the Bayesian approach. The practical applicability of Bayesian methods in the last 20 years has been greatly enhanced through the development of a range of approximate inference algorithms such as variational Bayes and expectation propagation, as well as posterior simulation methods based on the Markov chain Monte Carlo approach. As a result Bayesian methods have grown from a specialist niche to become mainstream. Therefore, we devoted a second part of the course to approximation tools, vitally important for Bayesian inference, and provide examples how to use Bayesian approaches to automatically select features, tune the regularization parameter in regression and classification, etc. For each problem, we introduce suitable Bayesian models and show how they are used to implement inference in the given data analysis problem. The last part of the course is devoted to Bayesian nonparametric models and methods, which have become widespread in the last 20 years. We discuss theoretical nonparametric Bayesian framework and then illustrate its application using the problems of clustering with unknown number of clusters, estimation of a latent subspace dimension, Gaussian process regression, etc.

Evgeny Burnaev  6  MA06129 
Biomedical Application of Photonics  Dmitry Gorin  3  MA03158 
Carbon Nanomaterials
The course covers the subject of carbon nanomaterials (fullerenes, nanodimond, nanotubes, and graphene). The history of carbon compounds since antiquity till our days starting from charcoal to carbon nanotubes and graphene will be reviewed. The students will have opportunity to synthesize carbon nanotubes (by aerosol and CVD methods) and graphene, to observe the materials in transmission (TEM) and scanning (SEM) electron microscopes as well as by an scanning tunnelling (STM) and atomic force (AFM) microscopes and to study optical and electrical properties of the produced carbon nanomaterials.

Albert Nassibulin  6  MA06044 
Cell Biology Lab Course
Lab course in Cell biology provides students an opportunity to explore how the techniques of molecular and cell biology may be used to understand cell function. Laboratory practice in cell biology will provide the experience in genetic manipulations with cell lines, immunostaining and fluorescence or confocal microscopy analysis. The main aspects for FACSanalysis and cell sorting will be introduced. The approaches for gene expression analysis by RTqPCR, Western blot and differential proteome analysis will be used to understand the influence of genetic manipulation to the cell function. The introduction in powerful approach to understand the protein interaction such as SPR optical biosensor will be provided.
The introduction in highthroughput screening of biologically active compounds will be provided. The course will provide students with a handson understanding of modern methods of cellular manipulation and understanding the mechanism of cell functioning. 
Olga Dontsova  6  MA06134 
Comparative Genomics  Mikhail Gelfand  3  MA03133 
Composite Materials and Structures
This course aims to provide knowledge about manufacturing, properties, and contemporary problems in composite materials. The emphasis is on the practical applications, theoretical background, and the use of composite materials in industry. The course cuts across several domains, covering mechanics of materials, design, manufacturing, and in service issues:
• Introduction: What is a composite? Classification. Metals vs composites, advantages and disadvantages. Applications in industry. Participants will learn fundamentals of these areas through active participation in teamwork. The course will provide practical knowledge on applications of composite materials in aerospace and mechanical engineering. 
Sergey Abaimov  6  MA06241 
Computational Science and Engineering II: Discretization
Many scientific models are formulated in terms of differential or integral equations and describe continuous quantities, such as the distribution of velocity of a fluid in a space outside an aircraft wing, distribution of stress in a solid body, price of a stock as a function of time, etc. In order to use these models in a computer simulation, the models must be discretized. The course covers a representative selection of methods of discretization of differential and integral equations. The emphasis of the course is on practical aspects of using discretization methods: intuitive understanding and formal derivation of accuracy of different methods, modelling, testing and optimizing real mechanical systems, and solving applicationsinformed practical problems.

Alexander Shapeev  6  MA06225 
Deep Learning
The course is about Deep Learning, i.e. a new generation of neural networkbased methods that have dramatically improved the performance of AI systems in such domains as computer vision, speech recognition, natural language analysis, reinforcement learning, bioinformatics. The course covers the basics of supervised and unsupervised deep learning. It also covers the details of the two most successful classes of models, namely convolutional networks and recurrent networks. In terms of application, the class emphasizes computer vision and natural language analysis tasks. The course involves a significant practical component with a large number of practical assignments.

Victor Lempitsky  6  PA06057 
Deep Learning
The course is about Deep Learning, i.e. a new generation of neural networkbased methods that have dramatically improved the performance of AI systems in such domains as computer vision, speech recognition, natural language analysis, reinforcement learning, bioinformatics. The course covers the basics of supervised and unsupervised deep learning. It also covers the details of the two most successful classes of models, namely convolutional networks and recurrent networks. In terms of application, the class emphasizes computer vision and natural language analysis tasks. The course involves a significant practical component with a large number of practical assignments.

Victor Lempitsky  6  MA06057 
Differential Topology  Alexander Gaifulin  3  MA06258 
Electrochemistry: Fundamentals to Applications
The course covers the subject of carbon nanomaterials (fullerenes, nanodimond, nanotubes, and graphene). The history of carbon compounds since antiquity till our days starting from charcoal to carbon nanotubes and graphene will be reviewed. The students will have opportunity to synthesize carbon nanotubes (by aerosol and CVD methods) and graphene, to observe the materials in transmission (TEM) and scanning (SEM) electron microscopes as well as by an scanning tunnelling (STM) and atomic force (AFM) microscopes and to study optical and electrical properties of the produced carbon nanomaterials.

Keith Stevenson  6  MA06127 
Energy Colloquium
The Energy Colloquium educates the audience in the presentday research and applications within the broader field of Energy Science and Technology. The Colloquium consists of a series of presentations by invited academic and industry speakers. The presentations target a nonspecialist audience.
All Master and Ph.D. students within the Energy Program are encouraged to attend the Energy Colloquium during the entire period of their studies. Students can earn 1 credit, if he/she participates in the Energy Colloquium over the course of any 2 terms of the academic year. Students who passed one round can make next (for credit) over the course of their subsequent studies. 
Alexei Buchachenko  1  MA04092 
English. Candidate Examinations
This is a metacourse which allows PhD students to register for English Qualification Exam for the Russian PhD Degree. There will be no lectures or seminars, only the exam. The preparatory course is also available in course catalog (look for "Academic Communication for PhD students" course).
The Exam has two parts: Part 1 – Preexam activities (Assignments 1, 2a, 2b) 
Elizaveta Tikhomirova  3  PE03003 
Functional Methods in The Theory of Disordered Systems
The course provides an extensive overview of contemporary functional methods in the theory of disordered systems. Starting from the theory of random matrices, it covers various aspects of electron motion in disordered media. The concept of the nonlinear supersymmetric sigma model is introduced and used as a unique language to describe such phenomena as energy level statistics, weak localization, renormalization group analysis, nonperturbative solution of the localization problem in quantum wires, electronelectron interaction, nonequilibrium phenomena in quantum dots.

Mikhail Skvortsov  3  MA06262 
Fundamentals of Device Physics
The course will provide a graduate level overview of physical principles of electronic and optoelectronic devices.

Vasili Perebeinos  6  MA06016 
Fundamentals of Remote Sensing  Evgeny Nikolaev  6  MA06186 
Gauge Theory and Gravitation
The present course could be also entitled 'Classical Field Theory', which menas it deals with all basic material needed in a study of fields preceeding to a study of their quantum properties. This requires in particular understanding such tools as Lagrangian, action functional, field equations (EulerLagrange equations). We shall also learn what are the most important symmetry principles which put certain constraints on a field theory. With this are related conservation laws. Typical important symmetries to mention are Lorentz and Poincare symmetry, conformal symmetry, gauge symmetry, general coordinate covariance.
A traditional approach to Classical Field Theory has a perfect base in the 2nd volume of LandauLifshitz' course. However, since that prominent book was written, new elements came forward, which required more knowledge of differential geometry and topology. In our lecture course, we shall get familiar with most important basic facts from these branches of mathematics with application to field theory. For example, understanding instantons (even at a classical level) requires good knowledge of a number of notions from modern math courses, such as vector bundles, connections, homotopy groups. Therefore our course has to go beyond the reach of LandauLifshitz' volume 2. 
Alexey Rosly  3  MA06178 
Geomatics for Earth 3D Reconstruction and Monitoring
Geomatics for Earth 3D Reconstruction and Monitoring Course description:
The course will present the basics of Geomatics, i.e. platforms, sensors and methodologies related to the collection, processing, analysis and interpretation of (2D/3D) data related to Earth’s surface. This includes platforms like satellite or drones, sensors like LiDAR or airborne cameras and techniques like photogrammetry, laser scanning, geodesy and topography. The goal is to introduce Geomatics with all its possible applications and potential.The lecture introduces the analysis of multitemporal images acquired from satellite borne imaging sensors both optical passive sensors and active Synthetic Aperture Radar systems. Advanced approaches to change detection will be illustrated that accounts for the imaging sensors technological development in terms of spatial, spectral, radiometrical and temporal resolutions. The class is divided into 7 parts: Introduction and background; taxonomy of change detection problems and applications; general concepts and data analysis architecture; change detection in multispectral optical images; change detection in SAR images; change detection in VHR images; supervised approaches and challenges in time series analysis. 
Fabio Remondino, Francesca Bolovo 
3  MA03197 
Geometrical Methods of Machine Learning  Alexander Bernstein  3  MA03169 
Geostatistics and Reservoir Simulation
The course includes lectures in geostatistics and reservoir simulation including fundamentals of single point and multipoint statistics, variance, and Gaussian simulation. The reservoir simulation lectures introduce the mathematics and practical portions of reservoir simulation. Laboratory computational exercises are also included.

Dmitri Koroteev  6  MA06085 
Hybrid Photonics  Pavlos Lagoudakis  6  MA03156 
Imaging in Biology
Overview of current imaging research techniques in basic biomedical research. Various applications in neurobiology, cancer biology and preclinical studies of novel and emerging advanced microscopy technologies. Analysis of experiments and research described in recent scientific papers. The introduction of the course also includes core mathematics, optics, and nuclear physics. Atop of studying different optical microscopy techniques and superresolution imaging the course will outline and compare the roles of CT (Computed Tomography), MRI (Magnetic Resonance Imaging), PET (Positron Emission Tomography) in biomedical research.
Topics also include clearing agents and techniques, optical imaging of brain activity in vivo using genetically encoded probes, immediate early gene mapping, intravital imaging, applications for functional analyses of neuronal circuits. The course aims to teach students to understand basic principles of the current imaging techniques, microscope design, and image formation. The course will also offer a practice in image analysis with open source software. Students will learn how to choose the most appropriate imaging method for their own research project. 
Dmitry Artamonov  6  MA06118 
Innovation and Intellectual Property Studies Doctoral Seminar
This course is a compulsory academic seminar series for all Ph.D. students in the Innovation and Intellectual Property Management Ph.D. Program. It consists of weekly research seminars that address the state of the art in research about the role of intellectual property in technological innovation. Specific topics and themes in the course will vary from year to year, but will typically include: theories of innovation; concepts and theories in IP management; practical issues in IP management; case studies in IP strategy; valuation of IP; Russian and international trends in intellectual property law; topics in technology entrepreneurship; product development and new technology; IP and design; patent analytics for innovation research; commercialization strategies of technology startups; organizational issues in technology innovation; conceptual issues at the interface of technology, science and business; public policy for technology, science and innovation; ethical and social issues related to IP and technological innovation; case studies in innovation management; philosophy of technology and philosophy of intellectual property; theory and methodology in IP management research; technology transfer and commercialization of university research; international collaboration and international trade in technology. As part of their seminar obligations, all students must prepare a formal written research paper on a topic that may or may not be directly related to their thesis research and make a presentation about the paper to the seminar group. The paper will be assessed.

Kelvin Willoughby  special  PC06009 
Integrable Systems 1  Igor Krichever, Anton Zabrodin 
3  MA06179 
Introduction to Product Lifecycle Management (PLM)
This newly developed course introduces Product Lifecycle Management (PLM) concepts and tools with concentration on practical examples of PLM Systems’ implementation in hightech industrial sectors. Students will be acquainted with major PLM systems on the market, their capabilities, market strategies of the providers, service arrangements, and with major customers. Historical perspectives and opportunities for implementation of these systems and tool will be addressed, discussed, and analyzed in the theoretical part of the course and in the students’ assignments. Invited lecturers will share their experience with introduction and use of PLM Systems in all phases of their companies’ business cycles. Students will discuss results and prospects of these systems’ use with representatives of these companies. A special sector of this course will be devoted to Configuration Management II – the basis for implementation of PLM in any business and/or design/development/manufacturing activities. Students, attending all sessions of this segment of the course will get official internationally recognized certificates of completion from the Configuration Management Institute (the U.S. leading organization in the development of standards and in certification of systems engineers). During the whole course, the students will work within Siemens Teamcenter environment while going through an extensive selfpaced training program in the Siemens PLM tools (LMS, NX, Technomatix). The students will learn basics of parametric and configuration optimization tools on an example of application of the P7 system. The students will apply obtained knowledge and skills in a two (earlier in the program defined) team assignments resulted in team presentations. An examination commission, consisting of CDMM faculty and of invited members, will conduct final evaluation of the overall product design completeness, quality of the results achieved, and of the team presentations delivered.

Ighor Uzhinsky  6  MA06148 
Materials and Devices for Nano and Optoelectronics  Valery Ryazanov  3  MA06206 
Methods for Enhanced Oil Recovery
Review of global oil resources and oil recovery technologies and mechanisms. Introduction to thermal oil recovery and EOR status. Heavy oil and oil sands: resources, reserves and recovery factor. Problems in heavy oil recovery and solutions. Comparison of recovery methods: nonthermal and thermal. Properties of rock, fluids, steam, steam additives, steamgas mixtures. Heat transfer: conduction heating (linear and radial). Steam injection systems. Formation heating: hot water and steam. Steamflooding: theory, OSR, patterns and mechanisms. Cyclic steam stimulation (CSS): variations, mechanisms and simplified prediction methods. Surface equipment and operation. Numerical simulation of steam injection processes: methods and limitations. Steam assisted gravity drainage (SAGD): principles, variations, field experience and limitations. Air injection based IOR processes, stoichiometry and kinetics. Laboratory and field performance evaluation of air injection based IOR processes. Field experience in Canada and the world.

Alexey Cheremisinm, Raj Mehta 
6  MA06117 
Modern Problems of Mathematical Physics  Andrei Marshakov  1.5  MA12268m 
Modern Problems of Theoretical Physics
The seminar "Modern Problems in Theoretical Physics" is a journal club meeting weekly to discuss a recent research paper of interest to the participants. The discussion is lead by one of the group members via a blackboard presentation. The goal of the seminar is twofold. From the one side, it assists the students in keeping track of interesting developments in the field of condensed matter physics. From the other side, it provides the group members with experience of thoughtful reading of original research papers and participation in scientific discussions, while helping them to shape their own interests.

Mikhail Feigelman, Konstantin Tikhonov 
1.5  MA12268p 
Molecular Biology Seminar
This seminar will cover original research papers on CRISPRCas from the period of 2003 to 2012, before the seminal advances that lead to development of genomic engineering. Each seminar will consist of in depth critical discussion of primary papers from the period given by two students in front of the rest of the class with particular attention given to research methodology and critical evaluation of the data. Papers send out to the class before the seminar to prepare for presentation/discussion.

Konstantin Severinov  3  MA03052 
Molecular Biology Seminar
This seminar will cover original research papers on CRISPRCas from the period of 2003 to 2012, before the seminal advances that lead to development of genomic engineering. Each seminar will consist of in depth critical discussion of primary papers from the period given by two students in front of the rest of the class with particular attention given to research methodology and critical evaluation of the data. Papers send out to the class before the seminar to prepare for presentation/discussion.

Konstantin Severinov  3  PA03052 
Natural Language Modelling and Processing
The main purpose of this course is to introduce the basic concepts needed for computational processing of human languages.
The course is aimed at understanding the specifics of Natural Language as an object of computational analysis, the ability to choose the proper linguistic model (linguistic features related to different levels of NL system) and the proper method to address the problem and carry out meaningful linguistic interpretation of results. By the end of this course the students should have clear understanding of the issues involved in the main tasks of document classification and text analysis. They will have to complete a miniproject aimed at providing a completed system for one of the tasks. These projects can be carried out both on the basis of open source technologies and in the frameworks of special scientific programs such as ABBYY Compreno Based Research, largescale Internet corpora (GIKR) projects or DialogueEvaluation NLPtesting tracks. 
Vladimir Selegey, Sergey Sharov 
6  MA06131 
NonLinear Optics  Arkady Shipulin  6  MA03154 
Numerical Methods in Continuum Mechanics  Oleg Vasilyev  6  MA06242 
OneDimensional Quantum Systems  Michael Lashkevich  3  MA06276 
Power Markets and Regulations
The course will introduce the students to power system economics. After covering fundamentals of microeconomics, main types of electricity markets and regulation will be discussed including the Russian market. Economic dispatch and Optimal Power Flow with Locational Marginal Pricing will also be covered. The lectures will be supplemented by a laboratory exercise utilizing PowerWorld simulation package and group miniprojects.

Janusz Bialek  6  MB06002 
Practicum in Experimental Physics  Valery Ryazanov  3  MA03208 
Principles of Applied Statistics  Alexey Naumov  6  MA06231 
Quantum Field Theory  Vladimir Losyakov  3  ME06011 
Quantum Mechanics  Semenov  3  MA06177 
Quantum Mesoscopics. Quantum Hall Effect  Igor Burmistrov  3  MA06278 
Quantum Optics  Zadkov and Yudson  3  MA03161 
RNA Biology
This course is devoted to the knowledge on the structures of RNA and RNAprotein complexes as well as their functioning in cells. The aim of this course is to provide an explanation of fundamental mechanisms such as translation, splicing and gene expression regulation based on the structural viewpoint. Thus the role of RNA in the maintenance of cell identity and cell metabolism will be defined. By focusing on modern techniques for RNA and RNAprotein structure and RNA modifications analysis, students will get aquainted with the approaches to study RNA input into cellular processes in vitro and in vivo.
The students will apply obtained knowledge and skills in presentations and a written exam. An examination commission, consisting of CTB faculty and of invited members, will conduct final evaluation of the overall product design completeness, quality of the results achieved, and of the presentations delivered. 
Timofey Zatsepin  3  MA03081 
Random Processes  TBD  3  ME06014 
Selected Topics in Energy: Physical, Chemical and Geophysical Challenges
The course provides an introduction to the modern topics related to fundamentals of exploration of energy resources, energy generation, storage, conversion and use. It identifies the corresponding practical challenges to be addressed at the fundamental research level and familiarizes the students with the stateoftheart approaches, methods and techniques in use in related scientific areas. The course seeks to emphasize and maintain interdisciplinary nature of the energyrelated topics, in particular, combination of micro and macroscopic approaches of geophysics, mechanics and chemistry in hydrocarbon exploration and development, relation between the physical and chemical processes of energy generation and conversion, integration of physical, chemical and mechanical approaches to perspective materials (physical and chemical synthesis, micro and macroscopic characterization, structureproperty relations, etc.) and related theoretical methodologies. These interdisciplinary links are mostly demonstrated by horizontal knowledge exchange among the students reporting and discussing practical examples from their own research field or from modern review or research publications. Topical lectures are included for further exploration of these links. The secondary aim of the course is the development of presentation skills (oral and writing), as well as scientific peerreview experience. The seminar format chosen for most activities allows students free exchange of knowledge and ideas, broader vision of their research projects and methodologies, better assessments of their own research skills and demands for further education.

Alexei Buchachenko  2  PA06106 
Sensors and Embedded Systems for Iot
This module will give a wideranging introduction to sensors and embedded systems in the scope of Internet of Things (IoT) paradigm. The module aims at providing full support to the nonengineering students with a series of carefully constructed concepts and exercises. It starts with setting the whole picture of IoT and its requirements for sensors and embedded systems. Then it introduces basic principles and simple projects, and moves towards more advanced IoT system design. Finally, the module will make overview of targeted applications including SmartX, Oil & Gas industry, wearables and medical applications.

Andrey Somov  3  MA03235 
Space Environment Data  Tatiana Podladchikova  6  MA06188 
Space Sector Course
This course examines the domain of space from multiple vantage points — space as a business, a way of life, a fulfillment of human dreams. In addition, it examines spacerelated issues that drive key international regulatory, economic, and global policy. To gain insight into these different dimensions, we examine space through three different lenses: subsectors, technologies, and organizations.Part 1: Sub Sectors:
Launch services and markets Satellite manufacturing and operations, including sensors and payloads Space data products Space communications and navigation services Space science payloads and missions Military space Human spaceflight, programs and policies For each one, we will discuss the organization of the subsector, what value it produces, how it is funded, the commercial and governmental organizations that participate, how it is regulated, and technology barriers Part 2: Technologies: Technology readiness, and sources of technology, technology planning Launch technologies and options Satellite technologies Payload technologies (may need to do in parts) Part 3: Organizations Space sector organizations (verticals and horizontals) “New Space” Space agencies and other international agents (NASA, ESA, etc.) 
Tatiana Podladchikova  6  MB06003 
Stochastic Modeling and Computations
The course shall be considered as a “soft” and selfcontained introduction to modern “applied probability” covering theory and application of stochastic models. Emphasis is placed on intuitive explanations of the theoretical concepts, such as random walks, law of large numbers, Markov processes, reversibility, sampling, etc., supplemented by practical/computational implementations of basic algorithms. In the second part of the course, the focus will shift from general concepts and algorithms per se to their applications in science and engineering with examples, aiming to illustrate the models and make the methods of solution clear, from physics, chemistry, machine learning, control and operations research discussed.
This course is recommended to M.Sc. and Ph.D. students planning to work on the subjects containing elements of uncertainty, irregularity or what is also called “stochasticity”. The “stochastic” subjects are prevalent in natural sciences (physics, chemistry, biology) or engineering disciplines (electrical, mechanical, chemical, industrial, etc). This course is to be conducted biannually. Tentatively during the 3rd or 4th (preferably) quarter of the year – to allow M.Sc. students from the first year to gaining access their needs (in the material of the course) during the first 23 quarters. The first execution of the course is planned for the spring of 2016. All necessary concepts from statistics, probability theory and statistical mechanics will be introduced in the course selfconsistently (no formal prerequisites in these disciplines are required). 
Michael Chertkov  6  MA06084 
Strings and Cluster Varieties
The course is directed to substantive work of the master and PhD students in order to understand recently found relations among supersymmetric gauge theories, refined topological strings, cluster varieties and integrable systems. The plan of wrk on the course consists of several introductive lectures on the various consistuents of the subject as well as student talks on recent original papers and results of their own investigation. The core topics include relation between cluster varieties and Painleve equations and approaches to the SeibergWitten theories with fundamental matter based on Toda systems and spin chains.

Andrei Marshakov  1.5  MA06176 
Technology Entrepreneurship  Kelvin Willoughby  6  MC06008 
Technology of Thin Films Deposition  Sergey Dorozhkin  3  MA03216 
Theoretical Foundations of Computer Science
In this course we introduce the cardinal topics of modern research in data science, and familiarize PhD students with fundamental solutions to research problems in this area. In particular, we introduce fundamental principles of data system architecture; we discuss massive data analysis, and we examine the management of very large data systems, including questions of adaptivity and selftuning; we present the fundamentals of data models and languages, especially in relation to semistructured data, multimedia, temporal and spatial data; we analyze the problems of privacy, security, and trust in data systems; we analyze techniques for recognition, image analysis, computer vision, statistical methods for learning, representations for recognition and localization. We investigate methods and algorithms for analyzing scientific data, social network analysis, recommender systems, mining sequences, time series analysis, online advertising, text/web analysis, topic modeling, mining temporal and spatial data, graph and link mining, rule and pattern mining. We introduce the concepts of dimensionality reduction and manifold learning, combinatorial optimization, relational and structured learning, classification and regression methods, semisupervised learning, unsupervised learning including anomaly detection and clustering, kernel methods, compressed sensing and sparse modeling, graphical models, Bayesian methods, deep learning, hyperparameter and model selection, Markov decision processes, reinforcement learning, dynamical systems and Hidden Markov Processes, recurrent networks.The course aims to bring all students on the same page regarding the nature and orientation of stateoftheart work in their field, so that they acquire both depth and breadth of knowledge.

Evgeny Burnaev  6  PA06140 
Thermal Fluid Science  Iskander Akhatov  6  MA06053 
Uncertainty Quantification
Uncertainty Quantification (UQ) marks a new approach to mathematical modelling and design at all levels. Instead of deterministic models, we consider randomized setup which can include uncertainties in model parameters, computational domains, inputs and many others. Thus, instead of a single quantity the probability distribution of the output parameter has to be studied, and many other associated tasks that include risk estimation, variance analysis. This also requires new computational tools that include the approximation of multivariate functions and computation of multidimensional integrals.

Ivan Oseledets  3  MA03226 
Vertex Operator Algebras
Infinitedimensional Lie algebras (such as Virasoro algebra or affine KacMoody algebras) turn out to be very important in various areas of modern mathematics and mathematical physics. In particular, they are very useful in the description of some field theories. In this context one arranges infinite number of the Lie algebra elements into a single object called field. This idea generalizes to the general theory of vertex operator algebras. VOAs capture the main properties of the infinite diemensional Lie algebras and have rich additional structure. Vertex operator algebras proved to be very useful in many situations; the classical example is the KP integrable hierarchy. They are also extensively used in modern algebraic geometry. Our goal is to give an introduction to the theory of vertex operator algebras from the modern
mathematical point of view. We describe the main definitions, constructions and applications of the theory. The course is aimed at PhD students and master students. 
Evgeny Feigin  3  MA06259 