Beijing-Novosibirsk seminar on geometry and mathematical physics ——Kostant, Steinberg, and the Stokes matrices of thett*-Toda equations

2020-07-03 17:00 zoom

Time: 2020-07-03 17:00 Beijing time (12:00 Moscow time, 16:00 Novosibirsk time)
Speaker: Ho Nan-Kuo (Department of Mathematics, NTHU)
We propose a Lie-theoretic definition of the tt*-Toda equations for anycomplex simple Lie algebra, based on the concept of topological-antitopological fusion which was introduced by Cecotti and Vafa. Our main result concerns the Stokes dataof a certain meromorphic connection, whose isomonodromic deformations are controlled by these equations. First, by exploiting a framework introduced by Boalch,we show that this data has a remarkable structure. It can be described using Kostant’stheory of Cartan subalgebras in apposition and Steinberg’s theory of conjugacy classesof regular elements, and it can be visualized on the Coxeter Plane. Second, we compute canonical Stokes data for a certain family of solutions of the tt*-Toda equationsin terms of their asymptotics.This is joint work with Martin Guest.
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