SMS scnews item created by Eduardo Altmann at Wed 15 May 2019 1334
Type: Seminar
Distribution: World
Expiry: 12 Jun 2019
Calendar1: 5 Jun 2019 1400-1500
CalLoc1: AGR Carslaw 829
CalTitle1: Triangular Schlesinger systems, Painleve VI equations, and superelliptic curves
Auth: ega@dora.maths.usyd.edu.au

Applied Maths Seminar

Triangular Schlesinger systems, Painleve VI equations, and superelliptic curves

Dragovic

Wednesday June 5, 2pm in the AGR room

Prof. Vladimir Dragovic (UT Dallas, USA)

Title: Triangular Schlesinger systems, Painleve VI equations, and superelliptic curves

Abstract: We study the Schlesinger system in the case when the unknown matrices of arbitrary size (p×p) are triangular and the eigenvalues of each matrix form an arithmetic progression with a rational difference q, the same for all matrices. We show that such a system possesses a family of solutions expressed via periods of meromorphic differentials on the Riemann surfaces of superelliptic curves. We determine the values of the difference q, for which our solutions lead to explicit polynomial or rational solutions of the Schlesinger system. As an application of the (2 × 2)-case, we obtain explicit sequences of rational solutions and one-parameter families of rational solutions of Painleve VI equations. This is a joint work with Renat Gontsov and Vasilisa Shramchenko.

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