Last updated: June 7, 2022

ICM regional satellite event

Japan forum associated with ICM 2022
RIMS Kyoto
June 13–14, 2022
https://www.mathsoc.jp/activity/meeting/JapanForum2022/
Summary
June 13 (Mon), 2022
Tadahisa Funaki (Univ. Tokyo/Waseda Univ./YMSC)

Hydrodynamic limit and stochastic PDEs related to interface motion
We consider several types of interacting particle systems at microscopic level, in which
particles move performing random walks with or without creation and annihilation depending on the situation. From these systems, via the hydrodynamic space-time scalinglimit or its nonlinear fluctuation limit, we derive three diﬀerent objects at macroscopic
level: the motion by mean curvature arising in phase separation phenomena, Stefan freeboundary problem describing segregation of species, and coupled KPZ equation which isa system of singular stochastic PDEs. These are all related to the problem of interface
motion. The Boltzmann-Gibbs principle plays a fundamental role. We also touch thediscrete Schauder estimate.
Yoshiko Ogata (Univ. Tokyo)

Classification of gapped ground state phases in quantum spin systems
Recently, classification problems of gapped ground state phases have attracted a lot ofattention in quantum statistical mechanics. We explain about operator algebraic approachto these problems.
Keita Yokoyama (Tohoku Univ.)

Reverse mathematics from multiple points of view
Reverse mathematics is a program in mathematical logic that was initiated by H. Friedmanin the 1970s and developed by S. Simpson and others. The aim of the program is to classify
mathematical theorems by comparing them with various types of axioms, typically setexistence and induction axioms in the formal system for the natural numbers and theirsubsets. The strength of axioms can be measured by several diﬀerent viewpoints, suchas consistency strength or computability strength, which are heavily connected to various
fields of mathematical logic. For example, consider the Peano existence theorem forordinary diﬀerential equations and the Hilbert basis theorem for polynomial rings. Thenthe former is stronger in the sense of consistency strength while the latter is stronger inthe sense of computability. Recently, the field of reverse mathematics has been widely
expanding with newer perspectives and techniques. In this talk, we overview the recent
developments of reverse mathematics and their connections to related fields.

1June 14 (Tue), 2022
Benoı̂t Collins (Kyoto Univ.)

Weingarten calculus and its applications
A fundamental property of compact groups and compact quantum groups is the existence
and uniqueness of a left and right invariant probability the Haar measure. This is a very
natural playground for classical and quantum probability, provided that it is possible
to compute its moments. Weingarten calculus addresses this question in a systematicway. The purpose of this talk is to survey recent developments, describe some salient
theoretical properties of Weingarten functions, as well as applications of this calculus
to random matrix theory, quantum probability and algebra, mathematical physics, andoperator algebras.
Hiroshi Iritani (Kyoto Univ.)

On decompositions of quantum cohomology D-modules
We discuss decompositions of quantum cohomology D-modules arising from various geometric settings. These decompositions can be related to semi-orthogonal decompositionsof topological K-groups via the Gamma integral structure.
Shu Kato (Kyoto Univ.)The formal model of semi-infinite flag manifolds
We explain our description of the formal model of semi-infinite flag manifolds as explicit
algebro-geometric objects, based on some recent developments in the representation theoryof aﬃne Lie algebras. We also discuss its consequences and perspectives.
Atsushi Ichino (Kyoto Univ.)

Theta lifting and Langlands functoriality
We review various aspects of theta lifting and its role in studying Langlands functoriality. In particular, we discuss realizations of the Jacquet-Langlands correspondence andthe Shimura-Waldspurger correspondence in terms of theta lifting and their arithmetic
applications.

Japan’s National Committeefor IMU

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