Representation Theory and applications to Combinatorics, Geometry and Quantum Physics

Massachusetts Institute Of Technology, Cambridge MA

Investigators

Abstract

The conference 'Representation Theory and Applications to Combinatorics, Geometry and Quantum Physics' will be held on December 13 through 19, 2013, at the Independent University of Moscow in Russia. It will be a major gathering of the leading mathematicians and young scholars whose work fits in the realm of representation theory. The conference has a broad scope and it aims to present some of the most important recent developments and techniques in this field, in particular the rich web of interconnections between representation theory, combinatorics, geometry, and physics, which has emerged in recent years and has greatly helped to advance each of these fields. The topics to be covered in the conference include algebraic groups, geometric representation theory, vertex algebras, infinite dimensional Lie algebras, combinatorics of plane partitions, conformal field theory and enumerative algebraic geometry. Many talks will involve applications of representation theory to mathematical physics, combinatorics and algebraic geometry. The organizers expect the conference to be a major gathering of researchers in these fields and one of the most important mathematical events to take place in Moscow in the last few years. We expect that it will attract many graduate students and postdoctoral fellows, especially from the USA. In quantum physics, which describes the world of small objects (such as atoms, electrons, nuclei, etc) the state of a physical system is random and not definitively determined, unlike classical physics. In other words, states are no longer definite points of the classical space of states, but rather functions on the space of positions of the system, whose squared magnitude represents the chance the system will be found in that particular state. Such functions can be added and multiplied by numbers; that is, they form what is called a linear space. Symmetries of the system act by linear transformations of this space and therefore play an important role in studying quantum systems. The part of mathematics which studies actions of symmetries in linear spaces is called representation theory since we represent symmetries by linear transformations. Representation theory is thus extremely useful in quantum physics and other areas of physics, while physics, in turn, constantly provides deep insights into representation theory and other areas of mathematics. For example, in recent years the development of the representation theory of infinite-dimensional symmetries, coming from quantum field theory, has been an active area of research. During the conference leading mathematicians and mathematical physicists, many from the United States, will discuss the connections between representation theory and related fields in mathematics, as well as the connections to physics, especially in light of recent breakthroughs. The conference will be very useful for young mathematicians and graduate students who will attend the conference. The money from this award will support the travel and local expenses of US-based speakers and participants. Conference materials will be disseminated through the conference website http://bogomolov-lab.ru/rep2013/, which will allow the ideas presented at the conference to be accessed by a wide audience in the US and around the world. NSF support from this award will be advertised on the website, and US-based participants will be able to apply for this support.