Analysis, PDE & Probability Seminar

Upcoming Seminars

2026. 5. 22 (Fri) 10:00-13:00  Room 8406
Raphael Danchin (Université Gustave Eiffel)

On the long-time behavior of global solutions of the Vlasov-Navier-Stokes equations

ABSTRACT. The incompressible Vlasov-Navier-Stokes system is a prototype model used to describe the dynamics of aerosols, i.e. suspensions of light particles in a surrounding viscous incompressible fluid. It comprises a kinetic transport equation for the particle distribution (depending on time, space, and kinetic variables) and the incompressible Navier–Stokes equations. These equations are coupled via a drag term known as the Brinkman force. Over the last two decades, a number of studies have focused on the mathematical analysis of these equations. Notably, it has been observed that, as with the classical Navier–Stokes equations, global weak solutions with finite energy exist for any finite energy data and uniqueness holds in dimension two. This course will review some recent results concerning the long-time behavior of these global solutions. It will be shown to differ significantly depending on whether the equations are considered in the whole space or under periodic boundary conditions.

2026. 5. 22 (Fri) 15:00-16:00  Room 1424
Kyungkeun Kang (Yonsei University)

Separation points of the Stokes equations with localized boundary data in the half space

ABSTRACT. We investigate the unsteady Stokes system in the half-space with boundary data that are localized in both space and time. We prove that certain boundary influxes can generate flow reversal in the interior of the half-space, meaning that at least one component of the velocity field changes sign. Our analysis is based on the representation formula for the half-space Stokes system and on pointwise estimates derived from the Green tensor associated with non-homogeneous boundary data. Using these tools, we construct solutions whose tangential velocity components experience at least one sign change. We further show that these solutions exhibit boundary separation at the boundary.

2026. 5. 29 (Fri) 14:00-15:00  Room 7323
Young-Heon Kim (University of British Columbia)

Lecture Series on Optimal Transport (I of III)

ABSTRACT. In these series lectures, we plan to discuss some basics of optimal transport theory, which gives a natural and geometric way to quantify differences between mass distributions; due to its geometric nature it has become an important tool in data analysis, with applications to AI. Some recent developments, including those in stochastic aspects of the theory will also be discussed.

2026. 6. 2 (Tue) 16:00-17:30  Room 8101
Mi Jung Park (University of British Columbia)

TBA

ABSTRACT. TBA

2026. 6. 5 (Fri) 14:00-15:00  Room 7323
Young-Heon Kim (University of British Columbia)

Lecture Series on Optimal Transport (II of III)

ABSTRACT. In these series lectures, we plan to discuss some basics of optimal transport theory, which gives a natural and geometric way to quantify differences between mass distributions; due to its geometric nature it has become an important tool in data analysis, with applications to AI. Some recent developments, including those in stochastic aspects of the theory will also be discussed.

2026. 6. 5 (Fri) 14:00-16:00  Room 1424
Seungchan Ko (Inha University)

Numerical Methods for Non-Newtonian Fluid Flows: From Finite Element Methods to Deep Learning

ABSTRACT. In this talk, we present a comprehensive study of both classical and modern numerical methods for solving partial differential equations (PDEs). We begin by employing finite element methods to solve fluid equations and subsequently delve into the theoretical analysis of the numerical method. In particular, we focus on a system of nonlinear PDEs that models the motion of an incompressible generalized Newtonian fluid with non-standard growth conditions. We construct a finite element approximation of the model and rigorously analyze the associated numerical method. Key technical tools include discrete counterparts of the Bogovskii operator, De Giorgi’s regularity theorem in two dimensions, and the Acerbi-Fusco Lipschitz truncation technique for Sobolev functions in function spaces with variable integrability exponents. As a natural extension of classical methods, we further explore modern approaches for solving PDEs using deep learning. Recent advancements in machine learning, particularly deep neural networks, have demonstrated remarkable success across various disciplines. In the second part of this talk, I will present my recent research on solving non-Newtonian fluid equations using deep learning. This method first computes the velocity using the Deep Ritz Method in a divergence-free formulation, and then recovers the pressure using Physics-Informed Neural Networks based on de Rham theory. I will also introduce a theoretical analysis of this new method.

2026. 6. 5 (Fri) 16:00-18:00  Room 1423
Catalina-Andreea Jurja (Universität Zürich)

Dispersion in a two-dimensional stratified fluid

ABSTRACT. The inviscid Boussinesq system is a widely used model in the study of oceanic flows, however, the description of its global dynamics remains an open problem. As a step towards understanding the long-time behaviour of its solutions, in this talk we will look at stability of a prototypical stratified steady state. In particular, the combined effect of gravity and stable stratification leads to a dispersive effect in the system for the perturbation and acts as a stabilising mechanism in the fluid. We will discuss the key properties of the perturbed system that allow for extended times of stability (from the local well-posedness timescale) as well as some elements of the proofs. This talk is based on joint works with Klaus Widmayer and Haram Ko.

2026. 6. 8 (Mon) 16:00-17:30  Room 1423
Hong Chang Ji (Sungkyunkwan University)

TBA

ABSTRACT. TBA

2026. 6. 12 (Fri) 14:00-15:00  Room 7323
Young-Heon Kim (University of British Columbia)

Lecture Series on Optimal Transport (II of III)

ABSTRACT. In these series lectures, we plan to discuss some basics of optimal transport theory, which gives a natural and geometric way to quantify differences between mass distributions; due to its geometric nature it has become an important tool in data analysis, with applications to AI. Some recent developments, including those in stochastic aspects of the theory will also be discussed.

2026. 6. 17 (Wed) 16:00-17:30  Room 1424
Young-Heon Kim (University of British Columbia)

Central Limit Theorems for Linear Eigenvalue Statistics of Random Geometric Graphs

ABSTRACT. Random geometric graphs are fundamental models of spatial networks, obtained by connecting nearby points of a Poisson point process. In contrast to Erdős–Rényi graphs, the underlying geometry induces strong local dependencies between edges, making spectral analysis substantially more difficult. In this talk, I will present central limit theorems for linear eigenvalue statistics of random geometric graphs. The proof combines techniques from stochastic geometry and Malliavin–Stein normal approximation.

Past Seminars

2026 Seminars
2025 Seminars
2024 Seminars
2023 Seminars
2022 Seminars
2021 Seminars
2020 Seminars
2019 Seminars

Organizers

Jae-Hwan Choi   -   Korea Institute for Advanced Study

Namhyun Eun   -   Korea Institute for Advanced Study

In-Jee Jeong   -   Korea Institute for Advanced Study

Yong-Gwan Ji   -   Korea Institute for Advanced Study

Nam-Gyu Kang   -   Korea Institute for Advanced Study

Taegyu Kim   -   Korea Institute for Advanced Study

Wontae Kim   -   Korea Institute for Advanced Study

Joonhyun La   -   Korea Institute for Advanced Study

Juyoung Lee   -   Korea Institute for Advanced Study

Se-Chan Lee   -   Korea Institute for Advanced Study

Deokwoo Lim   -   Korea Institute for Advanced Study

Sung-Jin Oh   -   UC Berkeley & KIAS

Junhee Ryu   -   Korea Institute for Advanced Study

Jinsol Seo   -   Korea Institute for Advanced Study

Young-Jin Sim   -   Korea Institute for Advanced Study

Kyeong Song   -   Korea Institute for Advanced Study

Jonguk Yang   -   Korea Institute for Advanced Study

Jaeyun Yi   -   Korea Institute for Advanced Study

Directions

Korea Institute for Advanced Study
Buildings 1 & 8, 85 Hoegi-ro, Dongdaemun-gu, Seoul, Korea



June E Huh Center for Mathematical Challenges
2nd Floor, 118 Hongneung-ro, Dongdaemun-gu, Seoul, Korea