Analysis, PDE & Probability Seminar

Upcoming Seminars

2026. 7. 21 (Tue) 16:00-17:30  Room 1424
Junhwa Jung (The Pennsylvania State University)

TBA

ABSTRACT. TBA

2026. 7. 22 (Wed) 16:00-17:00  Room 1423
Jakwang Kim (Chinese University of Hong Kong, Shenzhen)

Stability of Wasserstein projections in convex order via metric extrapolation

ABSTRACT. Optimal transport (OT) has been one of the most active research area in both pure and applied mathematical sciences. For its importance, there have been numerous variants and extOptimal transport (OT) has been one of the most active research area in both pure and applied mathematical sciences. For its importance, there have been numerous variants and extensions of it. One of them is "Martingale OT (MOT)", which is regarding OT with martingale constraint. This problem in particularly is studied for mathematical finance due to its relation to optional stopping. However, unlike classical OT, MOT does not always attain a solution. It is well known by Strassen that MOT has a solution if and only if two measures are in convex order, one of the most popular stochastic order in finance and economics. Recently, Gozlan and Juillet connect MOT with weak OT (WOT), and show that WOT value is the same as the projected distance onto "Convex order cone" with respect to a classical OT and related regularity. We prove the stability of Wasserstein projections in convex order based on metric extrapolation in Wasserstein space developed by Gallouët, Natale and Todeschi. In this talk, we provide MOT, its connection to mathematical finance briefly, and the sketch of the proof.

2026. 8. 3 (Mon) 15:00-16:00  Room 1423
Sewook Oh (GIST)

Maximal averages and non-transversality

ABSTRACT. Stein's spherical maximal function can be generalized to maximal averages over general hypersurfaces. Although this topic has been extensively studied, many problems still remain open. In this talk, I will present Lp estimates for maximal averages associated to hypersurfaces, with particular emphasis on the role of non-transversality.

2026. 8. 3 (Mon) 16:00-17:00  Room 1423
Juyoung Lee (KIAS)

Directional maximal operators in the plane

ABSTRACT. This talk investigates the Lebesgue boundedness of planar directional maximal operators D. These are maximal averages of functions over line segments in the plane whose slopes lie in a specified set P. A large body of multi-authored work has identified a geometric property of P, called finite-order lacunarity, as a key factor in ensuring that D is Lebesgue bounded. While several variations of this notion exist in the literature, they all center on the distribution of gaps in the slope set P. Building on earlier work, an article of Bateman (2009) asserted a dichotomy for such operators. Namely, D is bounded on L^p for all p>1, precisely when the slope set P is finite-order lacunary, or equivalently, when P does not admit Kakeya-type sets. Conversely, sublacunary direction sets P admit Kakeya-like phenomena, implying in turn that D is unbounded on L^p for all p>1. Recent work of Hagelstein, Radillo-Murguia, and Stokolos (2024) has identified a gap in the proof of this assertion and produced explicit counterexamples, revealing that the previously accepted characterization cannot hold as stated. We provide a rigorous resolution under an adjusted notion of admissible finite-order lacunarity.

2026. 8. 4 (Tue) 15:00-16:00  Room 1424
Haesung Lee (Kumoh National Institute of Technology)

On the existence, regularity and uniqueness of infinitesimally invariant measures

ABSTRACT. Infinitesimally invariant measures arise naturally in stochastic analysis when invariant measures of Markov semigroups, or limiting distributions of Markov processes, are studied through their infinitesimal generators. In Euclidean space, they can be described as positive measure-valued solutions to stationary Fokker-Planck equations written in double divergence form. We consider the existence of infinitesimally invariant measures for a given partial differential operator. We then discuss regularity properties of the density of such a measure, assuming its existence a priori, and explain uniqueness results obtained from recurrence of the associated Markov process. Finally, we present explicit computations of infinitesimally invariant measures for partial differential operators with special coefficient structures.

2026. 8. 4 (Tue) 16:00-17:00  Room 1424
Minjung Gim (National Institute for Mathematical Sciences)

TBA

ABSTRACT. TBA

2026. 8. 5 (Wed) 16:00-17:30  Room 1423
Soobin Cho (University of Illinois Urbana-Champaign)

TBA

ABSTRACT. TBA

2026. 8. 7 (Fri) 16:00-17:30  Room 1423
Hantaek Bae (UNIST)

TBA

ABSTRACT. TBA

2026. 8. 27 (Thu) 16:00-17:30  Room 1424
Jae-Hwan Choi (KIAS)

TBA

ABSTRACT. TBA

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