Special Seminar on Discrete Integrable Systems and Discrete Painlevé Equations（Feb. 19）
Abstract
This seminar will use the presence of Prof. Anton Dzhamay at WIAS as a Visiting Scholar as an opportunity to discuss recent progress in the areas of discrete integrable systems, discrete Painlevé equations and applications, in which he is an established expert. There will be an emphasis on the development and application of algebraic and geometric techniques, as well as discussion of the next steps and challenges in the field of algebraic and geometric approaches to discrete integrable systems.
Speakers
DZHAMAY Anton (Associate Professor, BIMSA)
Anton Dzhamay received his PhD from Columbia University under the direction of Professor Igor Krichever in 2000. After having postdoc and visiting positions at the University of Michigan and Columbia University, Anton moved to the University of Northern Colorado, getting tenure in 2011, becoming a Full Professor in 2016, and then transitioned to Emeritus status in 2025. In 2023–2024 Anton was a Visiting Professor at BIMSA, then became permanent BIMSA faculty in Summer 2024. His research interests are focused on the application of algebro-geometric techniques to integrable systems. Most recently he has been working on discrete integrable systems, Painlevé equations, and applications.
WILLOX Ralph (Professor, The University of Tokyo)
Ralph Willox received his Doctorate in Physics from the Free University of Brussels (VUB) in 1993 and joined the Graduate School of Mathematical Sciences at the University of Tokyo in 1998 as a JSPS Fellow, before being appointed Associate and then Full Professor. His research interests lie in integrable systems, particularly those that arise in mathematical physics. He has worked on algebraic techniques to construct solutions to integrable systems, discretization and ultradiscretization procedures, and methods for detecting integrability based on geometry and singularities.
KIM Wookyung (JSPS Postdoctoral Fellow, The University of Tokyo
Program
14:30-14:40 Opening
14:40-15:40 Lecture (Prof. DZHAMAY Anton)
15:40-15:50 Break
15:50-16:50 Lecture (Dr. KIM Wookyung)
16:50-17:00 Break
17:00-18:00 Lecture (Prof. WILLOX Ralph)
Titles and Abstracts:
[Prof. DZHAMAY Anton]
Title: Discrete Painlevé Equations with Constraints and Stabilizers of Simple Roots
Abstract: An important ingredient in the theory of discrete Painlevé equations with constraints on parameters (such as those corresponding to the existence of nodal curves on Sakai surfaces or arising in projective reductions) is the computation of subgroups of affine Weyl groups that stabilize particular subsets of simple roots. A general theory of how to do that was developed by Brink and Howlett and it can get quite complicated, but for examples related to discrete Painlevé equations it is relatively simple and quite neat. In this talk we consider how to visualize such computations with some applications to dynamics of discrete Painlevé equations with exotic symmetry types not explicitly appearing in the Sakai classification.
[Dr. KIM Wookyung]
Title: Integrable deformations of affine type A cluster maps associated with discrete sine–Gordon equations and discrete q-Painlevé VI
Abstract: In this talk, we consider the integrable deformation of the cluster map of affine type A_{3}^{(1)}, corresponding to the periodically reduced discrete sine-Gordon equation. We will demonstrate how this deformed map can be lifted, via Laurentification, to a cluster map whose coefficient dynamics in the Y-system correspond to the discrete q-Painlevé VI equation. We further show that this relation extends to generalized cases, namely a relation between the reduced discrete sine-Gordon equation and generalized q-Painlevé VI systems.
[Prof. WILLOX Ralph]
Title: The trouble with deautonomising higher order maps
Abstract: The deautonomisation of birational maps that have the singularity confinement property, i.e. the construction of nonautonomous versions of such maps that preserve the singularity properties of the original, has proven crucial in our understanding of the mathematical properties behind the integrability of second order maps.
For example, the deautonomisation procedure led directly to the development of a general theory of discrete Painlevé equations, and it seems highly likely it will play a crucial role in any future theory of higher dimensional Painlev¥’e equations as well. Generally speaking however, higher order integrable mappings may have non-confined singularities and it is important to understand if, and how, deautonomisation should work for such mappings.
In this talk we explore different deautonomisation scenarios on a series of carefully constructed higher order mappings, integrable as well as non-integrable, that possess non-confined singularities and we challenge some common assumptions regarding the co-dimensionality of the singular loci that might play a role in the deautonomisation process.
Date & Time
February 19, 2026 (Thu.) 14:30-18:00
Venue
Room #610, Building #19, Waseda Campus, Waseda University
Language
English
Prospected Audience
Graduate, Researchers, Faculty members
Organizer
Waseda University’s Institute for Advanced Study (WIAS)
Host
STOKES Alexander (Assistant Professor, WIAS)
Registration
Prior registration not required.
