The talk will consist of two 45-minute parts, with a short coffee break.
Abstract: The Whitham equations are the core of the perturbation theory of soliton systems. In the first part of the talk, we review the basics of the algebro-geometric integration theory of soliton equations and the setup for their perturbation. In the second part of the talk, we will discuss the Whitham theory for the isomonodromy equations for meromorphic connections with irregular singularities on algebraic curves. It will be shown that this theory provides a flat connection on the space of spectral curves of the Hitchin systems.
Igor Krichever received his doctorate under the guidance of S. P. Novikov at the Moscow State University. Currently he is a professor Columbia University, and one of the world leaders in the field of integrable systems. Several objects of contemporary mathematics bear his name, among others, the Krichever genus, and the Krichever-Novikov equation.
