HYKE meeting 2022

Date: August 29th(Monday)

Organizer:
박진영 Jinyeong Park (Hanyang University)

poster(pdf)

timetable

program

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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

poster(pdf)

program

timetable

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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).

Seminar in June 2021

1.
Time: 10th June (Thursday) 11:00 – 12:00
Speaker: Dr. Seongmin Jeon (KTH Royal Institute of Technology)
Place: #746, Natural Science Building, Hanyang University

Title : Almost minimizers for the thin obstacle problem

Abstract:
We consider Anzellotti-type almost minimizers for the thin obstacle (or Signorini) problem with zero thin obstacle. We discuss the regularity of the almost minimizers, as well as the regularity and structure of their free boundaries. The analysis of the free boundary is based on a successful adaptation of energy methods such as a one-parameter family of Weiss-type monotonicity formulas, Almgren-type frequency formula, and the epiperimetric and logarithmic epiperimetric inequalities for the solutions of the thin obstacle problem. This is joint work with Arshak Petrosyan.

2.
Time: 24th June (Thursday) 15:00 – 16:00
Speaker: Prof. Hyungjin Huh (Chung-Ang University)
Place: #746, Natural Science Building, Hanyang University

Title : Gradient flows related with $\alpha$-energy problem

Abstract:
We address a system of ODEs which is related with a particle system whose dynamics is governed by a gradient flow on the unit sphere associated with the $\alpha$ energy interaction potential between positions of all particles measured by a weighted distance $ |x_i -x_k |^{2\alpha + 2}$ for any $\alpha \neq -1$ and $\log |x_i -x_k |^2$ for $\alpha = -1$. Here we are interested in the repulsive coupling to study the equilibrium states and their stability. We mainly consider several case studies to obtain the qualitative insight.

HY-PDE workshop 2021

Date: May 26th(Wednesday) – 28th(Friday)

Organizers:
김승혁 Seunghyeok Kim, 박진영 Jinyeong Park

The workshop will be held online via zoom. If you want to attend the workshop, please contact the organizers.

Poster(pdf)

timetable

Program(title and abstract)

May 26th(Wed) May 27th(Thu) May 28th(Fri)
10:00 – 10:30 고동남 (가톨릭대) 정진욱 (서울대) 김유찬 (서울시립대)
10:35 – 11:05 최경수 (KIAS) 윤석배 (성균관대) 문병수 (인천대)
11:10 – 11:40 정인지 (서울대) 강문진 (KAIST) 서이혁 (성균관대)
Lunch
13:30 – 14:00 배한택 (UNIST) 최종근 (부산대) 곽철광 (이화여대)
14:05 – 14:35 이태훈 (KIAS) 김도현 (성신여대) 석진명 (경기대)
Coffee break
14:55 – 15:25 최범준 (KIAS) 최영필 (연세대) 옥지훈 (서강대)
15:30 – 16:00 배기찬 (서울대) 심우주 (서울대) 진상돈 (중앙대)

 

 

Intensive lectures on conformal field theory

We have the following lectures via google meet.

Title: Gaussian free field, conformal field theory, and SLE
Time:
May 10th (Monday) 11:00 – 12:00
May 11th (Tuesday) 11:00 – 12:00
May 12th (Wednesday) 11:00 – 12:00
May 13th (Thursday) 11:00 – 12:00
May 14th (Friday) 11:00 – 12:00
May 17th (Monday) 11:00 – 12:00
May 18th (Tuesday) 11:00 – 12:00

Speaker: Prof. Nam-Gyu Kang (KIAS)
Abstract:
In these lectures, I give an elementary introduction to conformal field theory in the context of probability theory and complex analysis. I consider statistical fields and define Ward functionals in terms of their Lie derivatives. Based on this approach, I explain some equations of conformal field theory and outline their relation to SLE theory.