Analysis, PDE & Probability Seminar

Upcoming Seminars

2024. 11. 22. (Fri) 10:00-11:00  Room 204 (Soorim)
Geunsu Choi (Sunchon National University)

Differentiability of Lipschitz maps on Banach spaces

ABSTRACT. We explore the differentiability and related concepts of Lipschitz maps defined on Banach spaces. In the context of norm attainment theory, we examine the nature of maximal derivative attaining Lipschitz maps and their approximations. If time permits, we also investigate the approximation by affine property in terms of maximal derivative.

2024. 11. 25. (Mon) 16:00-17:00  Room 204 (Soorim)
Hamin Jung (Seoul National University)

TBA

ABSTRACT. TBA

2024. 11. 27. (Wed) 11:00-12:30  Room 1424
Minjae Park (University of Chicago)

Brownian loops on non-smooth surfaces and the Polyakov-Alvarez formula

ABSTRACT. I will present a formulation of the Polyakov-Alvarez formula for non-smooth surfaces, expressed in terms of Brownian loops. This approach is motivated by earlier attempts to develop a heuristic understanding of Liouville quantum gravity (LQG) surfaces from a physics perspective. The result suggests that weighting specific regularized LQG surfaces by the partition function of the Brownian loop soup modifies the central charges in the expected manner. I will also discuss several open questions related to this framework. Based on joint work with Joshua Pfeffer and Scott Sheffield and the paper is available at https://www.sciencedirect.com/science/article/abs/pii/S0022123624002337

2024. 11. 29. (Fri) 16:00-17:50  Room 204 (Soorim)
Sanghyuk Lee (Seoul National University)

Strong unique continuation for the heat operator with potentials in weak spaces

ABSTRACT. This talk concerns the strong unique continuation property for the differential inequality $$|(\partial_t+\Delta)u(x,t)|≤V(x,t)|u(x,t)|,$$ where the potential $V$ belongs to suitable function spaces. In particular, we establish the strong unique continuation property for $V \in L^\infty_t L^{d/2,\infty}_x$, which has remained open since the earlier works of Escauriaza and Escauriaza--Vega. Our results are consequences of the Carleman estimates for the heat operator in the Lorentz spaces, which in turn are built on the spectral projection estimates for the Hermite operator.

2024. 12. 20. (Fri) 16:00-17:00  Room 1423
Youngtak Sohn (Brown University)

[HCMC Colloquium] Phase transitions of random constraint satisfaction problems

ABSTRACT. The framework of constraint satisfaction problems (CSPs) captures many fundamental problems in combinatorics and computer science, such as finding a proper coloring of a graph or solving Boolean satisfiability problems. To study the typical cases of CSPs, statistical physicists have proposed a detailed picture of the solution space for random CSPs based on non-rigorous methods from spin glass theory. In this talk, I will first survey the conjectured rich phase diagrams of random CSPs in the one-step replica symmetry breaking universality class. Then, I will describe the recent progress in understanding the global and local geometry of solutions, particularly in random regular NAE-SAT problem. This is based on joint works with Danny Nam and Allan Sly.

2024. 12. 26. (Thu) 10:30-12:00  Room 1424
Jinyeop Lee (University of Basel)

TBA

ABSTRACT. TBA

Past Seminars

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

Organizers

Yong-Gwan Ji   -   Korea Institute for Advanced Study

Mingu Jung   -   Korea Institute for Advanced Study

Nam-Gyu Kang   -   Korea Institute for Advanced Study

Seonwoo Kim   -   Korea Institute for Advanced Study

Joonhyun La   -   Korea Institute for Advanced Study

Jung-Kyoung Lee   -   Korea Institute for Advanced Study

Taehun 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

Jaehyeon Ryu   -   Korea Institute for Advanced Study

Jinsol Seo   -   Korea Institute for Advanced Study

Hyungsung Yun   -   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