Analysis, PDE & Probability Seminar

Upcoming Seminars

2025. 1. 23. (Thu) 15:00-16:00  Room 204 (Soorim)
Joonil Kim (Yonsei University)

Oscillatory integrals over global domains

ABSTRACT. Since Varchenko's seminal work, the asymptotics of oscillatory integrals and related problems have been effectively analyzed using the Newton polyhedra associated with the phase function $P$. These analyses have traditionally focused on integrals supported in sufficiently small neighborhoods. The purpose of this talk is to introduce the estimates of sub-level sets and oscillatory integrals over global domain $D$ with a primary focus on $D=\mathbb{R}^d$. In particular, we shall discuss (i) Piuseux series on $\mathbb{R}^2$ and resolutions of singularities, (ii) Analogue of Varchenko's theorem on the global domain (iii) Strichartz type inequality for dispersive partial differential equations (PDEs) as a key application. (iv) Phong and Stein's theorem regarding the global oscillatory integral operator (a joint work with Minbeom Kang)

2025. 1. 24. (Fri) 17:00-18:00  Room Online
Colin Petitjean (Gustave Eiffel University)

On curve-flat Lipschitz functions and their linearizations

ABSTRACT. Given two pointed metric spaces $M$, $N$, any basepoint-preserving Lipschitz map $f:M \to N$ can be associated with a canonical linearization $T_f:\mathcal{F}(M) \to \mathcal{F}(N)$, which is a bounded linear operator. The spaces $\mathcal{F}(M)$ and $\mathcal{F}(N)$ are known as Lipschitz free spaces over $M$ and $N$, respectively. A more or less recent trend explores the relationship between the properties of the nonlinear map $f$ and those of the linear operator $T_f$. In this talk, we will characterize the Lipschitz maps $f$ for which $T_f$ is a Dunford-Pettis operator (also referred to as completely continuous). If time permits, we will also discuss additional operator properties equivalent to the Dunford-Pettis property within this specific framework. This work is based on a collaboration with Gonzalo Flores, Mingu Jung, Gilles Lancien, Antonin Prochazka, and Andrés Quilis.

2025. 2. 6. (Thu) 10:30-11:30  Room 1423
Ho-Sik Lee (Universität Bielefeld)

Regularity results for nonlocal equations

ABSTRACT. By Green's representation formula, the gradient of the solution to Poisson's equation is pointwisely bounded by a Riesz potential of the right-hand side of the equation, the so-called gradient potential estimate. We show gradient potential estimates for nonlinear nonlocal elliptic equations from the joint with Prof. Lars Diening (Bielefeld), Kyeongbae Kim (SNU), and Dr. Simon Nowak (Bielefeld). Next, we consider examples of solutions that such higher differentiability estimates fail when the nonlocal equation has irregular coefficients, even in the homogeneous linear case. Inspired by Meyers' example, which is considered in [Meyers '63] and [Kh. Balci, Diening, Giova, Passarelli di Napoli '22], we give such examples of nonlocal equations. This is the joint work with Prof. Anna Kh. Balci (Charles), Prof. Lars Diening, and Prof. Moritz Kassmann (Bielefeld).

Past Seminars

2025 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

Juyoung Lee   -   Korea Institute for Advanced Study

Se-Chan 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