Seminar in May 2024

1.
Time: May 22nd (Wednesday) 10:30
Place: Natural Science Building #744
Speaker: Jaeyoung Yoon (Seoul National University)

Title: Measure-valued death state and local sensitivity analysis for Winfree model with uncertain high-order couplings

Abstract:
We study the measure-valued death state and local sensitivity analysis of the Winfree model and its mean-field counterpart with uncertain high-order couplings. The Winfree model is the first mathematical model for synchronization, and it can be cast as the effective approximation of the pulse-coupled model for synchronization, and it exhibits diverse asymptotic patterns depending on system parameters and initial data. For the proposed models, we present several frameworks leading to oscillator death in terms of system parameters and initial data, and the propagation of regularity in random space.

2.
Time: May 29th (Wednesday) 10:30
Place: Natural Science Building #744
Speaker: Seonwoo Kim (Korea Institute for Advanced Study)

Title: Hierarchical metastability structure in the reversible inclusion process

Abstract:
In this talk, I will discuss the hierarchical decomposition of metastability, which is ubiquitous in stochastic dynamical systems with complicated energy landscapes, and in particular the mechanism that triggers such a multi-scale phenomenon. Then, to fix ideas, I will focus on a specific example, the reversible inclusion process on a finite graph, where the hierarchical structure is based on the graph distance between the sites with maximum invariant measure. Then, I will briefly sketch the idea of proofs for the main theorems.

HYKE meeting 2022

Date: August 29th(Monday)

Organizer:
박진영 Jinyeong Park (Hanyang University)

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Venue

10:30 – 11:00 강명주 박사 (서울대)
11:00 – 11:20 조항준 (서울대)
11:20 – 11:50 정진욱 박사 (서울대)
Lunch
13:30 – 14:00 심우주 박사 (KIAS)
14:00 – 14:20 윤재영 (서울대)
Break
14:30 – 14:50 손성준 (성균관대)
14:50 – 15:20 이호 교수 (경희대)
Break
15:40 – 16:10 배기찬 박사 (서울대)
16:10 – 16:30 이명수 (성균관대)
16:30 – 16:50 변준혁 (서울대)

Seminar in July 2022

Time: July 8th (Friday) 10:30
Place: Natural Science Building #702
Speaker: Dr. Myeongju Kang (Seoul National University)

Title: Asymptotic behavior of various synchronization models and their continuum limit

Abstract:
Synchronous behaviors of oscillatory complex systems are ubiquitous in many biological and chemical systems, to name a few, firing of fireflies, synchronization of metronomes, rhythmic beating of pacemaker cells, etc. Famous examples are the Kuramoto model, which is a phase-coupled model, and the Winfree model, which is a pulse-coupled model. Both ode systems describe the time-evolutionary behavior of oscillators on one dimensional torus. Continuum limit is an effective approximation to describe a system with infinitely many particles using integro-differential equation.
In this talk, we first study the emergent dynamics of the particle models. Since solutions of the particle models become simple function valued solutions of the continuum models, analytical results on the time-evolutionary behavior of the particle models can be applied to analyze the continuum models. Especially, we study in what sense sequences of simple functions obtained from the particle models converge to solutions of the continuum models.

HY PDE workshop 2022

Date: July 18th(Monday) – 20th(Wednesday)

Organizers:
김승혁 Seunghyeok Kim, 박진영 Jinyeong Park

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Venue

July 18th (Monday) July 19th (Tuesday) July 20th (Wednesday)
10:00 – 11:00 이동현 (POSTECH) 문병수 (인천대) 고동남 (가톨릭대)
11:00 – 12:00 김도헌 (한양대) 이태훈 (KIAS) 김유찬 (서울시립대)
Lunch
13:30 – 14:30 옥지훈 (서강대) 윤석배 (성균관대) 최영필 (연세대)
14:30 – 15:30 김도현 (성신여대) 장진우 (POSTECH) 서이혁 (성균관대)
Break
15:40 – 16:40 김정호 (KIAS) 배한택 (UNIST) 최경수 (KIAS)
16:40 – 17:40 김성학 (경북대) 최범준 (POSTECH) 최우철 (성균관대)

Seminar in May 2022

Time: May 13th (Friday) 17:10
Place: Natural Science Building #702
Speaker: Prof. Dohyun Kim (Sungshin Women’s University)

Title: Asymptotic behavior for a system of Schrödinger equations

Abstract:
In this talk, we introduce a system for coupled Schrödinger equations, so-called Schrödinger-Lohe (SL) equation describing possible quantum synchronization. First, the recent progress on the SL equation with a specific focus on its emergent dynamics is presented by following a recent review article. Then, we provide a state-of-the-art result for the SL equation with heterogeneous wave functions. Precisely, convergence toward equilibrium is established when the coupling is dominant. Our strategy mainly depends on the method of dimension reduction and the dynamics of the Kuramoto model. This talk is based on the joint work with Dr. Hansol Park (Simon Fraser University).