Integrable Systems and Random Matrix Theory Seminar

The tt (topological-anti topological fusion) equations arose in the work of Cecotti and Vafa on supersymmetric quantum field theory, and the tt-Toda equations are a special case of these equations. Solutions of the tt*-Toda equations can be considered as certain isomonodromic deformations of meromorphic connections. They can be parametrized by two kinds of data. One comes from the asymptotic behavior of the solutions, and the other one comes from the monodromy including Stokes matrices. Two kinds of data correspond to each other via the Riemann-Hilbert correspondence. We will see that this correspondence is symplectic and give a generating function explicitly, and we will see an application to the constant problem. Speaker(s): Ryosuke Odoi (Waseda University)