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
Title : q-connection problems on hypergeometric and Painlevé equations
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
Title : Quantum Painlevé monodromy manifolds and Sklyanin-Painlevé algebra
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.
Title : Painlevé equations on weighted projective spaces
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.