Analysis, PDE & Probability Seminar

Upcoming Seminars

2026. 9. 11 (Fri) 11:00-12:00  Room 8406
Namkyeong Cho (Gachon University)

TBA

ABSTRACT. TBA

2026. 9. 18 (Fri) 16:00-17:30  Room 8101
Tuoc Phan (University of Tennessee)

TBA

ABSTRACT. TBA

2026. 10. 1 (Thu) 16:00-17:00  Room 수림(204)
Beomjun Choi (KAIST)

From Particles to Probability Distributions: Stability and Pattern Formation

ABSTRACT. Many problems in sampling and machine learning can be viewed as the evolution of large systems of interacting particles, representing samples, agents, or model parameters. At the microscopic level, their dynamics are described by ordinary or stochastic differential equations; at the macroscopic level, the corresponding probability distribution evolves according to a nonlinear PDE. This mean-field viewpoint connects probability, PDEs, optimal transport, particle systems, and machine learning. A central challenge is to understand their long-time behavior: Do they converge to a desired distribution? Which equilibria are stable, and when do instability or pattern formation occur? I will introduce this perspective through examples from sampling, aggregation equations, and mean-field learning dynamics, emphasizing the main ideas and sone open questions.

2026. 11. 12 (Thu) 16:00-17:00  Room 8406
Beomjong Kwak (KIAS)

Well-posedness of the nonlinear Schrödinger equation on a torus

ABSTRACT. TBA

2026. 12. 3 (Thu) 16:00-17:00  Room 수림(204)
Jaemin Park (Yonsei University)

Weak solutions and anomalous dissipation in two dimensional fluids

ABSTRACT. In this talk, I will discuss both classical and recent results on weak solutions to two-dimensional fluid equations. Although two-dimensional fluids are generally believed not to exhibit the same turbulent behavior as their three-dimensional counterparts, many fundamental properties, such as energy conservation and the zeroth law of turbulence, remain unclear for weak solutions, even in two dimensions. I will explain how such weak solutions can be constructed and investigate whether they conserve energy, highlighting several interesting open problems in this area.

Past Seminars

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

Organizers

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

Se-Chan Lee   -   Korea Institute for Advanced Study

Deokwoo Lim   -   Korea Institute for Advanced Study

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