Wednesday, July 9, 2025

2025-07-10 / 11:00 ~ 12:00

학과 세미나/콜로퀴엄 - Topology, Geometry, and Data Analysis:

by (규슈대학)

우리는 차원 축소 기법 중 하나인 Nonnegative Matrix Factorization (NMF)에 위상 정규화(topological regularization)를 결합한 Top-NMF를 제안한다. 기존의 정규화 기법들은 데이터 포인트 간의 관계를 최대한 보존하는 방식으로 차원 축소를 유도하는 반면, Top-NMF는 각 데이터 포인트를 함수의 관점에서 해석하고, 각 basis vector를 함수로 간주하여 그 support에 위상적 제약을 부여한다. 이를 위해 persistent homology를 통해 정의할 수 있는 다양한 위상 기반 정규화 항, 예를 들어 지속 에너지(Persistence Energy), 가중 지속 에너지(Weighted Persistence Energy), 클리크 편차 지표(Clique Deviation Metric) 등을 설계하고, 이를 NMF의 최적화 과정에 통합한다. 이를 통해 Top-NMF는 격자나 그래프와 같은 도메인이 갖는 위상적 속성을 반영하는 basis vector를 학습할 수 있게 한다.

2025-07-16 / 13:30 ~ 14:30

SAARC 세미나 - SAARC 세미나:

by 박상준()

Voiculescu's notion of asymptotic free independence applies to a wide range of random matrices, including those that are independent and unitarily invariant. In this talk, we generalize this notion by considering random matrices with a tensor product structure that are invariant under the action of local unitary matrices. Assuming the existence of the “tensor distribution” limit described by tuples of permutations, we show that an independent family of local unitary invariant random matrices satisfies asymptotically a novel form of independence, which we term “tensor freeness”. Furthermore, we propose a tensor free version of the central limit theorem, which extends and recovers several previous results for tensor products of free variables. This is joint work with Ion Nechita.

2025-07-09 / 16:30 ~ 17:30

학과 세미나/콜로퀴엄 - PDE 세미나:

by ()

In this talk, we present the global well-posedness for the cubic nonlinear Schrödinger equation for periodic initial data in the mass-critical dimension $d=2$ for large initial data in $H^s,s>0$. The result is based on a new inverse Strichartz inequality, which is proved by using incidence geometry and additive combinatorics, in particular the inverse theorems for Gowers uniformity norms by Green-Tao-Ziegler. In addition, we construct an approximate periodic solution showing ill-behavior of the flow map at the $L^2$ regularity. This is based on joint works with Sebastian Herr.

2025-07-09 / 15:30 ~ 16:30

학과 세미나/콜로퀴엄 - PDE 세미나:

by ()

In 2014, Bourgain and Demeter proved almost sharp decoupling inequalities for the paraboloid and the light cone, leading to various applications to the Schrodinger and the wave equations. I will explain some subsequent developments, including important contributions by Guth, Maldague and Wang, my joint work with Shaoming Guo, Zane Li and Pavel Zorin-Kranich, and joint work with Andrew Hassell, Pierre Portal and Jan Rozendaal.

Events for the 취소된 행사 포함