The 16th HU-SNU Joint Symposium on Mathematics
Date: November 11, 2023
Venue: Hokkaido University Conference Hall, Campus map (Conference Hall is located at the south-east corner, very close to the main gate)
Organizers: Akira Sakai (HU), Satoshi Masaki (HU), Takahiro Hasebe (HU), Hun Hee Lee (SNU), Panki Kim (SNU)
Program
10:00-10:30 Jean Carlos Nakasato (HU)
10:40-11:10 In-Jee Jeong (SNU)
11:20-11:50 Kuniyasu Misu (HU)
----- Lunch -----
14:00-14:30 Yuki Ueda (Hokkaido Univ. of Education)
14:40-15:10 Sung-Soo Byun (SNU)
15:30-16:00 Bruno Hideki Fukushima-Kimura (HU)
16:10-16:40 Jaehoon Kang (SNU)
Abstract
1) Jean Carlos Nakasato (HU)
Title: The Poisson problem in a thin domain with randomly oscillating boundary
Abstract: In this work we study the asymptotic behaviour of solutions of the Poisson equation posed in a thin domain with randomly rough boundary. We determine the effective problem depending on the roughness regime and also the rates of convergence. This is a joint work with F. P. Machado and M. C. Pereira.
2) In-Jee Jeong (SNU)
Title: Twisting in Hamiltonian Flows
Abstract: We prove that the twisting in Hamiltonian flows on annular domains, which can be quantified by the differential winding of particles around the center of the annulus, is stable to perturbations. In fact, it is possible to prove the stability of the whole of the lifted dynamics to non-autonomous perturbations, though single particle paths are generically unstable. These all-time stability facts are used to establish a number of results related to the long-time behavior of fluids and kinetic equations.
3) Kuniyasu Misu (HU)
Title: A game-theoretic approach to the asymptotic behavior of solutions to an obstacle problem for the mean curvature flow equation
Abstract: We consider the asymptotic behavior of solutions to an obstacle problem for the mean curvature flow equation by using a game-theoretic approximation, which we extend from that of [Kohn Serfaty 2006]. Kohn and Serfaty give a deterministic two-person zero-sum game whose value functions approximate the solution to the level set mean curvature flow equation without obstacle functions. We prove that moving curves governed by the mean curvature flow converge in time to the boundary of the convex hull of obstacles under some assumptions on the initial curves and obstacles. Convexity of the initial set, as well as smoothness of the initial curves and obstacles, are not needed. In these proofs, we utilize the properties of the game trajectories given by very elementary game strategies and consider reachability of each player.
4) Yuki Ueda (Hokkaido Univ. of Education)
Title: On the class of freely quasi-infinitely divisible distributions and an extension of Bercovici-Pata bijection
Abstract: We will talk about the class of freely quasi-infinitely divisible (FQID) distributions, which is an extension of the class of freely infinitely divisible distributions. Specifically, we will provide a construction for a certain family of FQID distributions and explain a positive answer to Bożejko's problem regarding the expansion of Bercovici-Pata bijection. This is a joint work with Ikkei Hotta, Wojciech Młotkowski and Noriyoshi Sakuma.
5) Sung-Soo Byun (SNU)
Title: Harer-Zagier type formulas for Gaussian Random Matrices
Abstract: Random matrix theory enjoys an intimate connection with various branches of mathematics. One prominent illustration of this relationship is the Harer-Zagier formula, which serves as a well-known example demonstrating the combinatorial and topological significance inherent in random matrix statistics. While the Harer-Zagier formula originates from the study of the moduli space of curves, it also gives rise to a fundamental formula in the study of spectral moments of classical random matrices. In this talk, I will introduce the Harer-Zagier type formulas for the classical Hermitian Gaussian random matrix ensembles and present recent results on these formulas for the non-Hermitian random matrix model called the Ginibre ensemble.
6) Bruno Hideki Fukushima-Kimura (HU)
Title: A Theoretical Approach to the Stochastic Cellular Automata Annealing and the Digital Annealer's Algorithm
Abstract: Finding a ground state of a given Hamiltonian of an Ising model on a graph G = (V,E) is an important but hard problem. The standard approach for this kind of problem is the application of algorithms that rely on single-spin-flip Markov chain Monte Carlo methods, such as the simulated annealing based on Glauber or Metropolis dynamics. In this work, we investigate new algorithms, the so-called Digital Annealer's algorithm, and some particular kinds of stochastic cellular automata, the SCA and the ε-SCA. We prove that if we consider exponential cooling schedules, the algorithms converge to approximations of ground states. We also provide some simulations of these algorithms and show their superior performance compared to the conventional simulated annealing.
7) Jaehoon Kang (SNU)
Title: Heat kernel estimates for symmetric jump processes with anisotropic jumping kernels
Abstract: We will discuss estimates of heat kernels for symmetric Markov processes on Euclidean spaces. We will first review heat kernel estimates for jump processes whose jumping kernels are comparable to isotropic functions. We will also check conditions that are equivalent to heat kernel estimates for jump processes. Then, we will consider jump processes with anisotropic jumping kernels and discuss their heat kernel estimates.