Web-seminar on Painlevé Equations and related topics

Next Seminar

19 November 2025 (Wed) 17:30～(JST)/9:30～(CEST/UTC+１)

Marta Mazzocco (Universitat Politècnica de Catalunya)
Today's talk is cancelled due to the speaker's illness. The talk will be rescheduled in January, 2026.

Special functions and quantum algebra

Abstract :
In this talk I will discuss how the theory of the sixth Painlevé equation can teach us many lessons on certain class of quantum algebras called Generalized Double Affine Hecke Algebras (GDAHA in short). In particular I will focus in the automorphisms of these algebras and their representation theory.

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)

Takuro Mochizuki (RIMS, Kyoto), Claude Sabbah (Ecole polytechnique), Yosuke Ohyama (Tokushima U.) , Szilard Szabo (Eötvös Loránd University,Budapest)

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.