Analysis, PDE & Probability Seminar

Upcoming Seminars

2025. 9. 24 (Wed) 16:00-17:00  Room 1423
Taegyu Kim (KIAS)

Classification of Blow-up Dynamics for the Calogero–Moser Derivative NLS

ABSTRACT. I will present recent progress on the study of finite-time blow-up dynamics for the Calogero–Moser derivative nonlinear Schrödinger equation (CM-DNLS). A central objective is to describe and ultimately classify the possible blow-up scenarios for this model. Along the way, several steps have been achieved: the construction of smooth chiral blow-up solutions (joint with Kihyun Kim, Soonsik Kwon), a soliton resolution result (joint with Soonsik Kwon), and the existence of smooth quantized blow-up solutions under symmetry restrictions (joint with Uihyeon Jeong). Building on these developments, in joint work with Uihyeon Jeong, Kihyun Kim, and Soonsik Kwon, we establish a classification of finite-time blow-up scenarios involving a single soliton for CM-DNLS. I will describe this classification result in detail and also briefly introduce some of the main ideas of the proof.

2025. 10. 27 (Mon) 16:00-17:00  Room 8309
Wontae Kim (KIAS HCMC)

TBA

ABSTRACT. TBA

2025. 10. 29 (Wed) 16:00-17:00  Room 1423
Jin Bong Lee (Seoul National University)

Strichartz estimates for Schr\"odinger equations over fractal time

ABSTRACT. In this talk, we introduce Strichartz estimates for the Schr\"odinger equations when time variable is restricted in a set of fractal dimension. We adopt a notion of Assouad dimension for an appropriate measurement for dimensionality. Using a locally constant property in time variable of solution to the Schr\"odinger equation, we reduce the problem to a discrete version of Strichartz estimates. Then, by a standard $TT^*$ method and the Assouad dimension, we prove the desired result. We also show some sharpness of our results.

2025. 11. 7 (Fri) 16:00-17:00  Room 1424
Seick Kim (Yonsei University)

TBA

ABSTRACT. TBA

2025. 11. 26 (Wed) 16:00-17:30  Room 8309
Kyeongsik Nam (KAIST)

Directed Polymers and Critical 2D Stochastic Heat Flow

ABSTRACT. The model of directed polymers provides a fundamental framework in statistical physics. The central challenge lies in understanding the universal statistical properties of the polymer's path and its partition function. This talk will provide an introduction to the general theory of directed polymers. We will then transition to a particular scaling limit: Critical 2D Stochastic Heat Flow, which emerges as the universal limit for two-dimensional directed polymers at a critical point.

2025. 11. 27 (Thu) 16:00-17:30  Room 8309
Kyeongsik Nam (KAIST)

Moments of Critical 2D Stochastic Heat Flow

ABSTRACT. Critical 2D Stochastic Heat Flow has been conjectured to display extreme intermittency, with h-th moments growing like exp(exp(h)). In this talk, we establish a lower bound of this conjecture. Joint work with Shirshendu Ganguly.

2025. 12. 3 (Wed) 16:00-17:30  Room 1423
Haesung Lee (국립금오공과대학교)

Analysis of linear elliptic equations with general drifts and $L^1$-zero-order terms

ABSTRACT. In this talk, we will discuss recent results on the homogeneous Dirichlet boundary value problem for linear elliptic equations in divergence form with general $L^p$-drifts and non-negative $L^1$-zero-order terms. By applying the divergence-free transformation, we establish the existence and uniqueness of bounded weak solutions. Under additional VMO and mild regularity assumptions on the diffusion coefficients, and for $L^s$-zero-order terms with $s \in (1,\infty)$, we further derive the existence and uniqueness of strong solutions for the corresponding non-divergence type equations. An important feature of this approach is that the divergence-free transformation enables us to compute the constants in the estimates explicitly, which can be effectively applied to error analysis.

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

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