주관: 권순식, 채명주

일시:   2024년 3월8일 ~ 9일

장소 및 숙소: 베스트웨스턴 플러스 세종, 세종시 어진동 https://www.hotelsejong.kr/ko

초청강연

김영헌(UBC, 2 talks).  An optimal transport approach to free boundary problems

Abstract:  In these two talks, we discuss how optimal transport, which is a theory for matching different distributions in a cost effective way, is applied to stochastic processes, then to free boundary problems. In particular, we focus on the Stefan problem which is a free boundary problem describing the interface between water and ice.  We consider the case where mass is carried by the stochastic process, and the transportation is determined by a stopping time, a random time for stopping the process. Our approach is related to the Skorokhod problem, a classical problem in probability regarding the Brownian motion.

최재환(KAIST)  An Introduction to SPDEs: Lecture 1

Abstract: In this talk, I will discuss the background knowledge necessary for understanding Sobolev regularity theory to the Parabolic Anderson Model (PAM). The concepts of random noises and solutions of PAM will also be explored.

서진솔(KIAS) An Introduction to SPDEs: Lecture 2

Abstract: In this talk, I will discuss the stochastic integral and L2 theory for the stochastic heat equation (SHE). I also introduce Lp theory for SHE and its application to the parabolic Anderson model.

곽범종(KAIST)  Strichartz estimates and global well-posedness of the cubic NLS on torus

Abstract: In this talk we present an optimal $L^4$-Strichartz estimate for the Schrödinger equation on the two-dimensional rational torus $\mathbb{T}^2$. We first recall the previously known results and counterexamples on the Strichartz estimates on the torus. Then we present our new Strichartz estimate, which has an optimal amount of loss, and small-data global well-posedness of (mass-critical) cubic NLS in $H^s,s>0$ as its consequence. An intuition on the relation between them is then provided. Our Strichartz estimate is based on a combinatorial proof. We introduce our key proposition, the Szemerédi-Trotter theorem, and explain the idea of the proof. This is joint work with S. Herr.

권도현(서울시립대)  Crystalline mean curvature flow with a volume constraint

Abstract: Atoms and molecules tend to minimize their surface energy, while crystals exhibit a preference for specific directions. The motion of sets by crystalline curvature arises from these physical phenomena, with sets evolving to reduce their anisotropic perimeter. In this talk, we discuss the crystalline mean curvature flow with nonlocal forcing given by a volume constraint. We show that a natural geometric property, associated with reflection symmetries of the Wulff shape, is preserved with the flow. Using a discrete-in-time approximation, we establish the global-in-time existence and regularity for a class of initial data with the reflection property. This talk is based on joint work with Inwon Kim, Eric Kim (UCLA) and Norbert Pozar (Kanazawa University).

심우주(경북대)  A deterministic Mean Field Game with velocity interactions

Abstract: In this talk, a mean field game model for pedestrians will be introduced, where each agent moves in a given domain and chooses their trajectories to minimize a cost including a penalization on the difference between their velocity and that of the other agents they meet. The main result of this study is the existence of an equilibrium of the given game in a Lagrangian framework and the regularity of its optimal curves.

윤혜원(KAIST)  Non-relativistic limit of modified scattering theory for the Boson star equations

Abstract: For Boson star equation and Hartree equation with Coulomb potential, modified scattering results are known by several literatures (for example, Pusateri `14 for Boson star, and Hayashi-Naumkin `98 or Kato-Pusateri `11 for Hartree). In this talk, we see that as the speed of light $c$ tends to infinity, the Hartree equation with Coulomb potential can be described by using Boson star equations. Especially, we focus on the convergence of asymptotic states (corresponds to the convergence of wave map in usual scattering theory) in their modified scattering results. This is joint work with 이기연(KAIST).

 

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