Perspectives in Representation Theory

Yale University, New Haven CT

Investigators

Abstract

The conference "Perspectives in representation theory" will be a meeting of mathematicians working in representation theory, with an emphasis on its relations to other subjects (notably, topology, algebraic geometry, number theory, and mathematical physics). The conference will be held on May 12-17, 2012 at Yale University, in honor of the 60th birthday of Prof. Igor Frenkel. The speakers have made and continue to make major contributions to the field, and are responsible for a vast web of connections of representation theory with other areas of mathematics and physics. The aim of the conference is to present current progress on the following (interrelated) topics: vertex operator algebras and chiral algebras, conformal field theory, the (geometric) Langlands program, affine Lie algebras, Kac-Moody algebras, quantum groups, crystal bases and canonical bases, quantum cohomology and K-theory, geometric representation theory, categorification, higher-dimensional Kac-Moody theory, integrable systems, quiver varieties, representations of real and p-adic groups, and quantum gauge theories. Thus the conference will be an occasion to discuss representation theory in the context of its connections with numerous other subjects, and to discuss some of the most recent advances in representation theory, including those which occurred thanks to application of techniques in other areas of mathematics and physics, including ideas from quantum field theory and string theory. Further details can be found on the conference website at http://www.math.yale.edu/frenkel60 Algebra is one of the oldest areas in mathematics. It encompasses a wide range of subjects from simple algebraic equations and polynomials to linear and abstract algebra. The study of symmetries is related to a branch of algebra called 'representation theory'. Representation theory has a vast array of applications in other areas of mathematics and physics. It is often through the study of representations that we learn about the innermost workings of our physical universe. While the origins of representation theory are algebraic, modern representation theory incorporates ideas from other branches of mathematics such as geometry, combinatorics, and category theory (a theory whose aim is to organize mathematical structure). These connections to new fields have both increased our knowledge in the area of representation theory as well as developed new applications of its ideas. The conference "Perspectives in representation theory" will be a gathering of some of the world's leading experts in this exciting field.