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

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.

Project Report

" held at Yale University on May 12-17, 2012 (dedicated to the 60th birthday of Professor Igor Frenkel). The conference reviewed the recent developments of representation theory, which is an area of mathematics that studies symmetries in linear space, and is closely connected with quantum physics. Representation theory, which originated at the end of 19th century, has seen rapid development in the last 30 years, thanks to ideas that came from geometry and form physics. The ideas from physics came form quantum field theory and string theory, namely from the subfield called "conformal field theory".Conformal field theory is a quantum theory of fields in a two dimensional spacetime which has an infinite dimensional collection of symmetries, which creates a rich environment for application of representation theory, and in fact many representation theoretic structures appeared from this circle of ideas. Another great source of ideas is the theory of quantum groups which appeared from the quantum Yang-Baxter equatiion, arising in field theory and statistical physics. Finally, huge breakthorughs in representation theory were achieved in the last 30 years by using ideas of categorification and methods of algebraic geometry. During the conference leading experts in the field reviewed the main developments in this field in the last 5 years, and outlined directions of further development, which constituted its intellectual merit. The conference attracted about 150 participants, most of them graduate students and young scholars. At least 35% of funding was used to support women, minorities, young scholars, and graduate students. The talks were recorded and put online, and a volume of proceedings has been published. This constitutes broader impacts of the project.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Type
Standard Grant (Standard)
Application #
1205125
Program Officer
Eric Sommers
Project Start
Project End
Budget Start
2012-02-01
Budget End
2013-06-30
Support Year
Fiscal Year
2012
Total Cost
$49,900
Indirect Cost
Name
Yale University
Department
Type
DUNS #
City
New Haven
State
CT
Country
United States
Zip Code
06520