Mathematical and Theoretical Physics

Master of Science Program

Skoltech CAS

The key features of the Mathematical and Theoretical Physics program are:

  • Cutting edge research in fundamental concepts of theoretical physics;
  • Covers the lack of joint education in physics and mathematics;
  • Special emphasis on research activity of students themselves;
  • Provides a unique educational environment in the fields of theoretical and mathematical physics; 
  • Renowned faculty with international experience and collaborations;
  • Incorporates a variety of disciplines covering major topics in mathematical methods;
  • Diverse and strong collaboration with international and Russian partners Publications in top journals.
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Key information

Program starts
September 2018
Modes and duration
Full time:
2 years
Tuition fees
No tuition fee
 for the applicants who pass the selection process

Application dates
All applicants:
Open: December 16, 2017

Awarded degree
Master of Science in Applied Mathematics and Physics
Language of instruction
Program is accredited by the Russian Government, certificate № 2568 from April 14, 2017. License № 2534 from February 7, 2017.

Field of Science and Technology
03.04.01 Applied Mathematics and Physics

Entry requirements

Relevant bachelor’s degree, or its equivalent in Mathematics, Applied Mathematics and Physics.

It is expected that applicants to Track A of the program should be able to demonstrate a knowledge of the following topics:
Basics of combinatorics, Elements of group theory, Linear algebra, Topology, Limits of sequences and functions, Derivatives and differentials, Geometry: affine and projective spaces, maps, second-order curves (conics), Complex analysis, Ordinary differential equations, Classical mechanics, Classical electrodynamics. (See the details here).

Applicants to Track B must demonstrate excellent knowledge of:
1. Quantum mechanics (in the scope of the Landau-Lifshitz course)
2. Mathematics (Calculus, Linear algebra, basic Complex analysis, Differential equations)
The entrance exam in Quantum mechanics is equivalent in complexity to the Landau theoretical minimum.

English language requirements
If your education has not been conducted in the English language, you will be expected to demonstrate evidence of an adequate level of English proficiency.

Solid knowledge of theoretical physics and ability to apply it in order to perform reliable calculations of real physical effects are crucially important for valuable interpretation of new experimental findings as well as for development of successful ideas towards new technological applications.

Aim and objectives
Program is aimed first and foremost at giving researchers a grounding in mathematics and deep knowledge of mathematical physics. It also offers students the chance to pursue in-depth study of the fundamental models of modern theoretical physics. Students are expected to take part in research projects alongside eminent specialists, teachers, and foreign colleagues specially invited to participate. The crux of our students’ scientific career involves compulsory scientific seminars and mandatory attendance at summer and winter scientific schools.

This program has no analogs abroad and can be compared only with the master’s program in Mathematical Physics at the Department of Mathematics of the Higher School of Economics (HSE). That said, the programs at Skoltech and HSE do not compete with each other. In fact, they complement each other. An agreement signed by Skoltech and the Higher School of Economics combines the programs and they are organized and run as a consolidated educational program.

The main scope of the Theoretical Physics program is to provide top-level education and professional training for specialists in the field of contemporary theoretical physics, with the emphasis on condensed matter theory. Solid knowledge of theoretical physics and ability to apply it in order to perform reliable calculations of real physical effects are crucially important for valuable interpretation of new experimental findings as well as for development of successful ideas towards new technological applications. Graduate of the program should have the skills of a modern researcher in this field and to meet the highest professional requirements of leading Russian and international research and educational centers. They must have a broad professional vision, know the relevant methodological approaches, and have sufficient skills to participate in research projects.

The program is realized in the network form with academic partners: the Moscow Institute of Physics and Technology and Landau Institute for Theoretical Physics.

Mathematical and Theoretical Physics MSc Program Structure


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Program Director
Igor Krichever Professor, Director of Skoltech Center for Advanced Studies

The key tenets of our Mathematical and Theoretical Physics educational program are compulsory scientific seminars (including student seminars) and a strong scientific community. Students study tailored, individual courses approved by their supervisors, who determine the range of selected courses depending on the specific area of the student’s scientific study. We put emphasis on students’ independent scientific study that encourages their rapid fundamental scientific (and thus career) growth. Curriculum.

Learning and professional outcomes

Track A:
A successful graduate of the program will know and be able to:

  • Apply mathematics and modern methods of theoretical physics to the most advanced problems of present fundamental science;
  • Use high level of mathematical education (in algebraic geometry, topology, representation theory) and theoretical physics (quantum field
    theory, integrable systems, statistical mechanics and complex systems etc.) to continue successful career in most of popular directions in
    science and technology;
  • Apply the culture of scientific discussion and ability of carrying scientific research to function in scientific research community or
    multidisciplinary team;
  • Continue education and research within the PhD program at Skoltech and leading leading scientific centers in Russia and abroad.

Track B:
A successful graduate of the program will know and will be able to use:

  • Mathematical methods of contemporary theoretical physics, including: complex analysis, topology, functional integrals, multi-dimensional asymptotic methods;
  • Analytical methods and approaches to the broad range of physical problems: phase transitions (classical and quantum), thermodynamics and kinetics of mesoscopic systems and nanostructures, quantum field theory, hydrodynamics, quantum transport of charge, spin and heat, quantum-coherent effects in macroscopic systems, including qubit’s theory and engineering.


Main research directions:

Track A:

  • Topology;
  • Algebraic geometry;
  • Representation theory;
  • Symplectic geometry;
  • Category theory;
  • Integrable systems;
  • Supersymmetric gauge theories and conformal theories.

Track B:

  • Mesoscopic electronic systems;
  • Superconducting hybrid structures;
  • Quantum phase transitions;
  • Quantum Hall effect;
  • Spintronics;
  • Quantum magnetism and topological order;
  • Physics of quantum computation.

Career paths:

  1. PhD positions in academic & research institutions;
  2. Specialist positions in various economy sectors including Skolkovo resident companies and startups.

Academic partners:

Track А:

Track B:


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