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List of Talks

Szilard Szabo (Budapest Univ. of Technology and Economics)

10 March 2021 (Wed)   17:30~(JST)/9:30~(UTC+1)

Asymptotic analysis of non-abelian Hodge theory in rank 2
Abstract : First we explain how recent results on the asymptotic solutions of Hitchin's equations on a curve allow one to prove Simpson's Geometric P = W conjecture in the Painlevé 6 case. In the second part of the talk we outline the main ideas of our ongoing work on the extension of this result to the Garnier case with 5 parabolic points.

Yousuke Ohyama (Tokushima University)

10 February 2021 (Wed)   17:30~(JST)/9:30~(UTC+1)

Title : q-connection problems on hypergeometric and Painlevé equations PDF
Abstract: We study connection problems of q-Painlevé equations. This problem is divided Into three parts:
1. Study q-connection problems on hypergeometric equations
2. Study q-connection problems on linearized equations of the Painlevé equations
3. Consider q-connection problems on the Painlevé equations

Marta Mazzocco (University of Birmingham)

27 January 2021 (Wed)   17:30~(JST)/9:30~(UTC+1)

Title : Quantum Painlevé monodromy manifolds and Sklyanin-Painlevé algebra PDF

Abstract : In this talk, I will discuss the quantisation of the Painlevé monodromy manifolds as a special class of quantum del Pezzo surfaces. In particular I will introduce the generalised Sklyanin-Painlevé algebra and characterise its PBW/PHS/Koszul properties. This algebra contains as limiting cases the generalised Sklyanin algebra, Etingof-Ginzburg and Etingof-Oblomkov-Rains quantum del Pezzo and the quantum monodromy manifolds of the Painlevé equations.

Hayato Chiba (Tohoku University)

13 January 2021 (Wed)   17:30~(JST)/9:30~(UTC+1)

Title : Painlevé equations on weighted projective spaces  PDF
Abstract : The weight of a differential equation is defined through the Newton diagram of the equation. It gives the weighted projective space, that is the natural compactification of the phase space of a differential equation. In this talk, I show how to construct a weighted projective space, analysis of the Painlevé equation using the geometry of a weighted projective space, and related topics.