Analysis, PDE & Probability Seminar

2026 Seminars

2026. 1. 28 (Wed) 16:00-17:00  Room 1423
Junkee Jeon (Kyunghee University)

Stochastic Control and Free Boundary Problems Arising in Financial Mathematics

ABSTRACT. In this presentation, I discuss stochastic control problems arising from financial mathematics. Specifically, I address problems that combine stochastic control with optimal stopping, as well as those involving singular control and switching control. Furthermore, I investigate a two-person zero-sum game played between a singular controller and an optimal stopper. A key focus of this talk is deriving the associated parabolic variational inequalities and analyzing the analytic properties of the free boundaries they induce. I will also explain how these boundaries characterize the optimal strategies. Finally, I illustrate the application of these models in finance with numerical examples.

2026. 1. 14 (Wed) 16:00-17:00  Room 1423
Kihoon Seong (Cornell University)

Sine–Gordon measures, topological soliton, and Gaussian multiplicative chaos

ABSTRACT. I will discuss the sine–Gordon QFT, which lies in the same universality class as the Coulomb gas and the XY model, and exhibits the BKT phase transition (Nobel prize 2016). The sine–Gordon action admits infinitely many homotopy classes. Even though the action has no energy minimizers in homotopy classes with high topological charge, I will show that the Gibbs measure nevertheless concentrates and exhibits Ornstein–Uhlenbeck fluctuations around the multi-soliton manifold. I will then discuss the geometry of this multi-soliton manifold, including how solitons are arranged, such as their expected locations and gaps. Furthermore, I will explain the asymptotics of the partition function using Gaussian multiplicative chaos. Based on joint work with Hao Shen and Philippe Sosoe.

Past Seminars

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

Organizers

Jae-Hwan Choi   -   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

Jung-Kyoung Lee   -   Korea Institute for Advanced Study

Juyoung Lee   -   Korea Institute for Advanced Study

Se-Chan Lee   -   Korea Institute for Advanced Study

Sewook Oh   -   Korea Institute for Advanced Study

Sung-Jin Oh   -   UC Berkeley & KIAS

Hyangdong Park   -   Korea Institute for Advanced Study

Junehee Ryu   -   Korea Institute for Advanced Study

Jinsol Seo   -   Korea Institute for Advanced Study

Kyeong Song   -   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