Next Seminar
23 July 2025 (Wed) 17:30～(JST)/10:30～(CEST/UTC+2)
Szilard Szabo (Technical University of Budapest)
Rank three representations of Painlev\'e systems: wild character varieties and Fourier--Laplace transformation
Abstract :
We give explicit cubic equations for the wild character varieties corresponding to the rank 3 representations of Painlev\'e equations, and compare them to the ones of their classical rank 2 representations. We prove that Fourier--Laplace transformation induces a hyperKaehler isometry between corresponding Hodge moduli spaces.
Painlevé Seminar Topics
Recently, we have encountered many interesting links between differential
equations of Painlevé types and other fields of mathematics such
as algebraic geometry, non-abelian Hodge theory and topological recursion
and so on.
In this web seminar, we will organize research talks on Painlevé
equations and related topics on web (zoom), basically about once every
two or three weeks.
From September 2022, Regular time for seminar talk will be on Wednesday from 17:30--18:30 + discussion time
in JST(Japan) or 10:30--11:30 in UTC+1. We are looking forward to your participation in
the seminar. In order to get zoom access, please register through the form.
List of Talks
You can find the titles and abstracts of all seminars. ⇒ List of Talks
Registration
Online. Please register at the form, we will send you about web seminar address.
Organizers
Arata Komyo (Hyogo), Frank Loray (Rennes 1),
Ryo Ohkawa (Osaka Metropolitan), Masa-Hiko Saito (Kobe Gakuin), Takafumi Matsumoto (RIMS, Kyoto)
Scientific Committee (other than the Organizing Committee)
Supported by
French ANR-16-CE40-0008 project "Foliage" (Frank Loray)
JSPS Grant-in-aid (A) 22H00094 (PI: Masa-Hiko Saito)
Osaka Central Advanced Mathematical Institute:
MEXT Joint Usage/Research Center on Mathematics and Theoretical Physics JPMXP0619217849.
Joyce structures were introduced by T. Bridgeland in the context of the space of stability conditions of a three-dimensional Calabi-Yau category and its associated Donaldson-Thomas invariants, and have also appeared in the context of isomonodromic systems associated with Painlevé equations. Under certain non-degeneracy conditions, they encode a complex hyperkähler structure on the tangent bundle of the base of the Joyce structure. Taking inspiration from this work, I'll give a description of (real) hyperkahler metrics compatible with an integrable system structure that is very similar to the description of Joyce structures. In particular, I will give examples of such hyperkähler metrics where there is a precise analog of the Plebański function appearing in the context of Joyce structures. This is work in progress, which is a follow-up to https://arxiv.org/abs/2403.00548.