HY-PDE workshop 2021

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

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.



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)
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
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)
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.

Intensive lectures on quantum information theory

We have the following lectures via google meet.

Title: Quantum information theory
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)
우선, 직관적으로 이해할 수 있는 고전정보이론의 기초를 설명하고, 그와 대응되는 양자정보이론의 기초를 설명한다. 이를 통해, 고전정보와 양자정보의 유사점과 차이점에 대해서 알아본다.

Seminar in April 2021

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

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.

Online seminar in February 2021

We have the following seminar via google meet.


Title: Convergence of first-order consensus-based global optimization algorithms
Time: February 17th (Wednesday) 10:00 – 10:40
Speaker: Dr. Doheon Kim (KIAS)
Recently, consensus-based optimization (in short CBO) methods have been introduced as gradient-free optimization methods capable of tackling non-convex objective functions. Until recently, the convergence study for CBO methods was carried out only on their corresponding mean-field limits, Fokker-Planck equations, which do not imply the convergence of the CBO method per se. In this talk, we study convergence analysis for first-order CBO methods, without resorting to the corresponding mean-field models.



Title: A singular limit of the Chern-Simons-Higgs model
Time: February 17th (Wednesday) 10:45 – 11:25
Speaker: Dr. Bora Moon (Seoul National University)
In this talk, we consider the singular limit of the Cauchy problem for Chern-Simons-Higgs model that suggests a correspondence between the model of Chern-Simons-Higgs and Chern-Simons-Schrodinger. More precisely, we prove that when the velocity of light goes to infinity (the so-called ‘non-relativistic limit’), a class of time-dependent solutions of the modulated Chern-Simons-Higgs system converges to the corresponding solution of the Chern-Simons-Schrodinger system globally in time under the assumption of suitable initial data.

Online seminar in January 2021

We have the following seminar via google meet.


Title: Uniform-in-time continuum limit of the lattice Winfree model and emergent dynamics
Time: January 13th (Wednesday) 10:00 – 10:40
Speaker: Myeongju Kang (Seoul National University)
Abstract: We study a uniform-in-time continuum limit of the lattice Winfree model(LWM) and its asymptotic dynamics which depends on system functions such as natural frequency function and coupling strength function. The continuum Winfree model(CWM) is an integro-differential equation for the temporal evolution of Winfree phase field. The LWM describes synchronous behavior of weakly coupled Winfree oscillators on a lattice lying in a compact region. For bounded measurable initial phase field, we establish a global well-posedness of classical solutions to the CWM under suitable assumptions on coupling function, and we also show that a classical solution to the CWM can be obtained as a $L^1$-limit of a sequence of lattice solutions.



Title: Emergence of consensus on the Stiefel manifold
Time: January 13th (Wednesday) 10:45 – 11:25
Speaker: Dr. Dohyun Kim (Seoul National University)
Abstract: In this talk, we introduce first-order and second-order high-dimensional Kuramoto models on the Stiefel manifold which extend the previous consensus models on Riemannian manifolds including several matrix Lie groups. For the proposed models, sufficient frameworks leading to complete and practical consensus are provided in terms of the initial data and system parameters. On the other hand, we propose a consensus-based algorithm for nonconvex optimization on the Stiefel manifold. For a given objective (or target) function on the Stiefel manifold, we construct a stochastic interacting particle system for sample points which are expected to converge to a single point, which is close enough to a global minimizer.



Online seminar in November 2020

We have the following seminar via google meet.


Title: Introduction to Deep Q Learning and its application to finance
Time: November 23th (Monday) 09:30 – 10:10
Speaker: Prof. Chanho Min (Ajou University)
This seminar introduces the Deep Q Learning, one of the most popular methods of reinforcement learning and their application to finance problems. Reinforcement learning is a popular model of the learning problems through trial-and-error interactions in a certain given environment. This seminar will discuss the mathematical formulation of Deep Q learning and how each component plays a crucial role in agent learning. Finally it provides real world application in finance, and shows how reinforcement learning can outperform humans even with limited data.



Title: Hamilton-Jacobi-Bellman equations for maximum entropy optimal control
Time: November 23th (Monday) 10:15 – 10:55
Speaker: Dr. Jeongho Kim (SNU)
Abstract:In this talk, we introduce an entropy-regularized optimal control problem for the deterministic control system. We derive dynamic programming principle and corresponding the Hamilton-Jacobi-Bellman (HJB) equation, which is regularized version of the HJB equation of the classical optimal control problem. After deriving the HJB equation, we provide several mathematical properties of it, including asymptotic convergence. We also provide an explicit example of control-affine problem, in which the optimal control is given as a normal distribution. Finally, we test the maximum entropy optimal control framework to several numerical examples, illustrating the benefit of the maximum entropy framework.


Online seminar in August 2020

We have the following seminar via google meet.

Title: 출근 지하철 혼잡도 분산을 위한 최적 수도권 지역 분할
Time: August 6th (Thursday) 09:30 – 10:10
Speaker: Dr. Wonse Kim (SNU)
출근 지하철 혼잡도 분산을 위한 최적 수도권 지역 분할본 연구는 수도권 전철 네트워크 데이터와 지하철 승객 승, 하차 빅데이터를 분석하여, 출퇴근 지하철 차내 혼잡도를 낮추기 위한 수도권 지역 최적 분할 방법을 제시한다. 구체적으로, (1) Dijkstra Algorithm 에 기반한 Dial Algorithm 을 사용하여 수도권 전철의 출근시간대 차내 혼잡도를 계산하고 (2) 지하철역 위치정보를 활용하여 출근시간 혼잡 구간을 지나는 승객의 지하철 최초 탑승 지역을 파악한다. (1), (2)의 결과를 바탕으로, 수도권 전철 출근시간 혼잡구간의 혼잡도를 최소화 시키는 수도권 지역 최적 분할을 찾기 위한 손실함수 (loss function)을 새롭게 정의하고, 이를 최적화 시킴으로서 최적 수도권 지역분할을 찾는다. 본 연구의 결과는 2차 코로나 대유행을 앞둔 현 시점에서, 정책 당국자들로 하여금 2부제 재택근무와 같은 사회적 거리두기 방법의 효과를 극대화 시킬 수 있는 구체적인 가이드 라인을 제시할 것으로 기대된다.

Title: Thermodynamic Cucker-Smale ensemble on complete Riemannian manifolds
Time: August 6th (Thursday) 10:15 – 10:55
Speaker: Dr. Woojoo Shim (SNU)
We study emergent collective behaviors of a thermodynamic Cucker-Smale(TCS) ensemble on complete smooth Riemannian manifolds. For this, we extend the TCS model on the Euclidean space to a complete smooth Riemannian manifold by adopting the work for a CS ensemble, and provide a sufficient framework for velocity alignment and thermal equilibrium formulated in terms of a priori assumptions on network topology and the uniform continuity of relative velocities. As a concrete example, we also study emergent dynamics of the TCS model on the unit d-sphere and hyperbolic d-space by removing a uniform continuity assumption on the relative velocities in the proposed sufficient framework for a general setting. In particular, asymptotic dynamics of the proposed TCS model on the unit 2-sphere and hyperbolic plane exhibits a dichotomy, either convergence to zero velocities or approach toward a geodesic.

Title: From the Lohe Tensor Model to the Lohe Hermitian Sphere Model and Emergent Dynamics
Time: August 6th (Thursday) 11:00 – 11:40
Speaker: Hansol Park (SNU)
We study emergent behaviors of the Lohe hermitian sphere (LHS) model which is an aggregation model on $\mathbb C^d$. The LHS model is a complex analogue of the Lohe sphere model on $\mathbb R^d$, and hermitian spheres are invariant sets for the LHS dynamics. For the derivation of the LHS model, we use a top-down approach, namely a reduction from a high-rank aggregation model, the Lohe tensor model. The Lohe tensor model is a first-order aggregation model on the space of tensors with the same rank and sizes, and it was first proposed by the authors in a recent work [J. Stat. Phys., 178 (2020), pp. 1268–1292]. In this work, we study how the LHS model appears as a special case of the Lohe tensor model, and for the proposed model, we provide a cross-ratio-like conserved quantity, a sufficient framework for the complete aggregation, and a uniform $\ell^p$-stability estimate with respect to initial data.