Analysis, PDE & Probability Seminar

Upcoming Seminars

2024. 4. 23. (Tue) 17:00-18:00  Room Online
Melissa Tacy (University of Auckland)

A quasimode approach to spectral multipliers

ABSTRACT. A central question of Euclidean harmonic analysis is; when does a multiplier $$ Mf = \mathcal{F}^{-1}[m(\cdot)\mathcal{F}[f](\cdot)] $$ defined as an operator $L^2 \to L^2$ extend to a bounded operator $L^p \to L^q$? The Bochner-Riesz multipliers where $$ m_{R}(\xi)=\left(1-\frac{|\xi|^{2}}{R}\right)_{+}^{\delta} $$ are one well-known example of these type of operators. On manifolds we can consider analogous questions about whether spectral multipliers $M(\sqrt{\Delta})$ are bounded. Such questions have been long known to be connected to the growth properties of quasimodes (approximate solutions) to the eigenfunction equation $\sqrt{\Delta}u=\lambda u$. In this talk we will see how we can formalise the relationship between growth properties of quasimodes and boundedness of spectral multipliers and use the relationship to obtain new results about the latter.

2024. 4. 25. (Thu) 16:00-17:00  Room Online
Linjie Zhao (Huazhong University of Science and Technology)

Equilibrium perturbations for stochastic interacting systems

ABSTRACT. In this talk, we consider equilibrium perturbations for two specific interacting particle systems: the generalized exclusion processes and the one-dimensional chain of anharmonic oscillators. By adding a small perturbation to the equilibrium profile and speeding up the process under proper scaling, we show the perturbed quantities evolve according to the Burgers equation in the exclusion process, and to two decoupled Burgers equations in the anharmonic chain, both in the smooth regime. The proof uses the relative entropy method. The talk is based on joint work with Lu Xu.

2024. 4. 25. (Thu) 17:00-18:00  Room Online
Shledon Dantas (University of Valencia)

Norm-attaining lattice homomorphisms

ABSTRACT. In this talk, we will be discussing the structure of the set ${\rm Hom}(X, \mathbb{R})$ of all lattice homomorphisms from a Banach space $X$ into $\mathbb{R}$ in terms of norm-attaining elements. It turns out that every lattice homomorphism defined on classical Banach lattices ($c_0$, $L^p$-spaces, and $C(K)$-spaces) attains its norm, which shows, in particular, that there is no James theorem for this class of functions. We also discuss the existence of a lattice homomorphism which does not attain its norm and also Bishop-Phelps type theorems in the Banach lattice setting.

2024. 5. 3. (Fri) 16:00-17:10  Room 1424
Ki-Ahm Lee (Seoul National University)

TBA

ABSTRACT. TBA

2024. 5. 23. (Thu) 16:00-17:00  Room Online
Shuta Nakajima (Meiji University)

Upper tail large deviation for the one-dimensional frog model

ABSTRACT. In this talk, we study the upper tail large deviation for the one-dimensional frog model. In this model, sleeping and active frogs are assigned to vertices on $\mathbb{Z}$. While sleeping frogs do not move, the active ones move as independent simple random walks and activate any sleeping frogs. The main object of interest in this model is the asymptotic behavior of the first passage time $T(0,n)$, which is the time needed to activate the frog at the vertex $n$, assuming there is only one active frog at $0$ at the beginning. While the law of large numbers and central limit theorems have been well established, the intricacies of large deviations remain elusive. Using renewal theory, Bérard and Ramírez have pointed out a slowdown phenomenon where the probability that the first passage time $T(0,n)$ is significantly larger than its expectation decays sub-exponentially and lies between $\exp(-n^{1/2 + o(1)})$ and $\exp(-n^{1/3 + o(1)})$. In this article, using a novel covering process approach, we confirm that $1/2$ is the correct exponent, i.e., the rate of upper large deviations is given by $n^{1/2}$. Moreover, we obtain an explicit rate function that is characterized by properties of Brownian motion and is strictly concave. This talk is based on joint work with Van Hao Can, Naoki Kubota.

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

Jaehun Lee   -   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

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