Title: Integrable Systems and Canonical Bases
Speaker: Harold Williams
Speaker Info: UC Berkeley
Brief Description:
Special Note:
Abstract:
We argue that the Hamiltonians of certain Toda-type integrable systems should be understood as elements of a generalized canonical basis. To make this precise, we will describe a Jacobian algebra associated with the Poisson structure on a simple Lie group, and explain how the computation of characters of Lie group representations can then be mapped in a nontrivial way onto the computation of quiver grassmannians associated with this algebra. After working some examples of this correspondence, we'll explain how this result fits into a broader context motivated by 4d N=2 field theory, irregular Hitchin systems, and the theory of cluster algebras.Date: Thursday, March 06, 2014