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

Organizers:
김승혁 Seunghyeok Kim, 박진영 Jinyeong Park

poster(pdf)

program

timetable

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Venue

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).

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.

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)

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.

We have the following lectures via google meet.

Title: Quantum information theory
Time:
April 26th (Monday) 13:00 – 14:00
May 4th (Tuesday) 13:00 – 14:00
May 11th (Tuesday) 13:00 – 14:00

Speaker: Prof. Soojoon Lee (Kyung Hee University)
Abstract:
우선, 직관적으로 이해할 수 있는 고전정보이론의 기초를 설명하고, 그와 대응되는 양자정보이론의 기초를 설명한다. 이를 통해, 고전정보와 양자정보의 유사점과 차이점에 대해서 알아본다.

Time: 8th April (Thursday) 13:00 – 14:00
Speaker: Dr. Jinwook Jung (Seoul National Univertisy)
Place: #702, Natural Science Building, Hanyang University

Title : On the pressureless damped Euler-Riesz equations

Abstract:
In this talk, we analyze the pressureless damped Euler–Riesz equations posed in either the whole space or periodic domain. We construct the global-in-time existence and uniqueness of classical solutions for the system around a constant background state. We also establish large-time behaviors of classical solutions showing the solutions towards the equilibrium as time goes to infinity. In the whole space case, we first show the algebraic decay rate of solutions under additional assumptions on the initial data compared to the existence theory. We then refine the argument to have the exponential decay rate of convergence even in the whole space. In the case of the periodic domain, without any further regularity assumptions on the initial data, we provide the exponential convergence of solutions.