Whittaker Functions, Crystal Bases, and Quantum Groups

The Banff International Research Station will host the "Whittaker Functions, Crystal Bases, and Quantum Groups" workshop from June 6 to 11, 2010.

This workshop plans to focus on intriguing relationships between two fields of mathematics, number theory and representation theory, and some connections to mathematical physics. Number theory is one of the oldest branches of mathematics. It studies properties of the whole numbers and fractions as well as more exotic constructions, and today finds many applications in computer science and cryptography. Representation theory, a more recent development, is a comprehensive tool to understand deeper symmetries in mathematical phenomena, and today plays an indispensable role in many fields of mathematics and physics. Although these branches of mathematics sound wildly different, it turns out there are many fascinating relationships between them. This workshop plans to focus on one such relation embodied in Whittaker functions. These are special and highly symmetric functions that have traditionally appeared when one applies representation theory to number theory as in the theory of automorphic forms. Recently new connections between number theory and representation theory via these functions have been uncovered, connections that link number theory with exciting constructions in representation theory called crystal bases and quantum groups. This workshop will investigate these connections by bringing together a group of researchers drawn from several fields, including physics, with the hope of building new bridges between these subjects.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the US National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnologí­a (CONACYT).

BIRS Scientific Director, Nassif Ghoussoub
E-mail: birs-director[@]birs.ca
http://www.birs.ca/~nassif