Prof Tudor Ratiu
April 21, 2014, 13.30 – 15.00
Beijing-1 Auditorium, China cluster
Skolkovo School of Management
SEMINAR ABSTRACT:
In spite of is ubiquity in nature, a rigorous mathematical definition of symmetry has emerged only in the late 19th century. Ever since, symmetry has been at the center of many scientific and technological developments. In mathematics, symmetry plays nowadays a central role and has generated an enormous body of knowledge in the pure areas. With few exceptions, mainly in theoretical physics, symmetry considerations have not entered the mainstream in applied areas till the end of the 20th century. In this talk, I will give several examples where symmetry considerations have led to remarkable results in applied areas, in the context of conservative systems. The workhorses are the momentum map and the associated symmetric reduction theory, objects from symmetric symplectic and Poisson geometry that have given rise to deep insights in pure mathematics and are in the process to reshape many applied areas. Several basic equations of motion in theoretical physics are obtained from fundamental principles by a symmetry reduction process. This has immediate consequences in the analysis of these equations and their numerical simulations. Symmetry turns out to be also the glue that ties together such diverse areas as fluid mechanics and computational anatomy. The basic models of liquid crystal dynamics are based on complicated symmetries that are crucial for their understanding. The falling cat rotational motion at zero angular momentum, a possible model of spacecraft docking, is explained using symmetry considerations from gauge theory.
SPEAKER INTRODUCTION:
Tudor Ratiu is Chaired Professor of Mathematics at the Swiss Institute of Technology in Lausanne and Founding Director of the Bernoulli Center. He obtained his Ph.D. at the University of California, Berkeley, in 1980. He then spent three years as a T.H. Hildebrandt Research Assistant Professor at the University of Michigan in Ann Arbor and then joined the Mathematics Department of the University of Arizona, Tucson. Four years later he took a Professor position at the University of California, Santa Cruz, where he stayed till his 1998 appointment in Lausanne. He was an NSF postdoctoral, Sloan Foundation, Fulbright, and, recently, was elected an AMS Fellow. He held a Miller Research Professorship at Berkeley and a Humboldt Senior Professorship in Germany. He won the Ferran Sunyer i Balaguer Prize of the Catalan Mathematical Society for his book “Momentum Maps and Hamiltonian Reduction”, joint with Juan-Pablo Ortega, and was awarded the Medal “Star of Romania”.
Tudor’s main interests are in geometric mechanics, mathematical physics, continuum mechanics, Hamiltonian dynamics, stability and bifurcation theory, global analysis, geometric integration, evolutionary PDEs, control theory, integrable systems, symplectic and Poisson geometry, Lie theory, and infinite dimensional geometry. He has published over 200 papers and seven books (one of them translated into both German and Chinese), and has given over 320 invited talks. His research investigates the role of symmetry in nature. All his work, including his most abstract, is motivated by applications. This has led him to both pure and applied mathematical areas and to close collaboration with physicists and engineers.
