WS4
Asymptotic Expansion of τ-functions
and Related Topics
Asymptotic Expansion of τ-functions
and Related Topics
The workshop "Asymptotic Expansion of τ-functions and Related Topics" will be held at RIMS, Kyoto, Japan, 17th-21th February 2025. It is a part of RIMS project 2024 "Development in Algebraic Geometry related to Integrable Systems and Mathematical Physics". The purpose of this workshop is to bring together leading researchers in the fields of Painlevé equations and related subjects, to present their cutting-edge research results, and to discuss them with researchers and graduate students.
The Painlevé equations are a class of nonlinear ODEs that were discovered in the course of exploring special functions that generalize hypergeometric functions and elliptic functions. They are an important subject of study, as they are connected to various topics in mathematics and physics such as isomonodromic deformations, affine Weyl group symmetries, and the algebraic and symplectic geometric structures of their initial value spaces, matrix models, and so on. In these relationships, the τ-functions, which is analogous to θ-functions, play particularly significant roles.
Since the discovery in 2012 of an explicit formula for the asymptotic expansion of the τ-function of the Painlevé VI equation using conformal field theory, research aimed at investigating the structure of τ-functions associated with the general solutions of the Painlevé equations has become increasingly active. Progress has also been made in studying the τ-function using methods such as irregular conformal blocks, Nekrasov partition function, and topological recursion. In recent years, new approaches for studying the quantization of τ-functions have also been proposed.
However, many research challenges remain, including the comparison of τ-functions constructed using various approaches, their relationship with (wild) character varieties via the Riemann-Hilbert correspondence, connection problems, and more. The aim of this workshop is to promote discussions among researchers studying various aspects of the Painlevé equations by introducing the latest research results and unsolved problems, with the goal of achieving a deeper understanding of the properties of the τ-functions.
Davide Dal Martello (Rikkyo University)
Harini Desiraju (University of Sydney)
Benedetta Facciotti (University of Birmingham)
Pavlo Gavrylenko (SISSA, Trieste)
Martin Guest (National Taiwan University & Waseda University)
Michi-aki Inaba (Nara Woman's University)
Kohei Iwaki (University of Tokyo)
Oleg Lisovyy (University of Tours)
Toshiyuki Mano (University of the Ryukyus)
Marta Mazzocco (Catalan Institution for Research and Advanced Studies (ICREA), Barcelona & Universitat Politècnica de Catalunya (UPC) & University of Birmingham)
Yuma Mizuno (University College Dublin)
Haruki Nakagawa (Kanazawa University)
Hajime Nagoya (Kanazawa University)
Andrii Naidiuk (University of Tours)
Takahiko Nobukawa (Kobe University)
Hidetaka Sakai (University of Tokyo)
Yoshitsugu Takei (Doshisha University)
Satoshi Tsuchimi (Kobe University)
Yasuhiko Yamada (Kobe University)
RIMS, Kyoto University
JSPS Grant-in-Aid for Scientific Research (A) 22H00094 (PI: Masa-Hiko Saito)
JSPS Grant-in-Aid for Challenging Research (Exploratory) 22K18669(PI: Masa-Hiko Saito)
JSPS Grant-in-Aid for Challenging Research (Exploratory) 23K17654 (PI: Kohei Iwaki)
JSPS Grant-in-Aid for Scientific Research (B) 24K00525 (PI: Kohei Iwaki)
Group Photo (2025/02/20)