Shift-of-argument algebras in geometry and representation theory

Abstract: Integrable systems first came to prominence as a geometric abstraction of structure in classical mechanics. Despite these origins, integrable systems have been found to interact meaningfully with pure mathematics. Modern examples include the role such systems play in the Langlands program, mirror symmetry, and quantum cohomology. On the other hand, Mishchenko-Fomenko systems represent another paradigm of integrable systems in pure mathematics. They exhibit the kind of Lie-theoretic symmetry that allows difficult geometric problems to be posed and solved entirely in algebraic terms. The algebraic incarnations of Mishchenko-Fomenko systems are the so-called shift-of-argument algebras, which enjoy connections to geometry and representation theory.

I will give a non-technical overview of the themes mentioned above. Some emphasis will be placed on work in progress with Iva Halacheva and Valerio Toledano Laredo.

combinatoricscategory theoryrepresentation theory

Audience: researchers in the topic

( slides )

The TRAC Seminar - Théorie de Représentations et ses Applications et Connections