Title: The Hitchin System, the Airy Equation, the Trefoil, and a Cluster Variety
Speaker: Eric Zaslow
Speaker Info: Northwestern University
I will try to connect some of the topics in the title through a concrete example, the trefoil. This knot represents the link-at-infinity of a curve given as y^2 = cubic polynomial in x. When that curve appears as the spectral curve in a Hitchin system on the complex plane, the growth rate of the associated flat sections near infinity is encoded by a related knot. This data feeds into the construction of various moduli spaces, all isomorphic and equal to the A_2 cluster variety. The cluster structure can be understood from the various perspectives.Date: Thursday, October 9, 2014
This talk represents a collection of observations, not all new and too loose to be considered "work in progress." They have emerged from discussions with Vivek Shende, David Treumann, Andy Neitzke and Linhui Shen.