Tuesday, August 12, 2025

2025-08-14 / 14:00 ~ 15:30

학과 세미나/콜로퀴엄 - 기타: 대수곡선, 리만곡면에 대한 여름 개별연구 발표회

by 6인의 학생(KAIST)

6 students (four advanced undergraduate students and two first year graduate students) present their summer study results on the subject of algebraic curves and Riemann surfaces. The topic include: - On sheaves and cohomology over topological spaces. - On relationship between divisors and line bundles on compact Riemann surfaces. - On holomorphic vector bundles on compact Riemann surfaces. - On Cech cohomology of sheaves on compact Riemann surfaces. - On Serre duality theorem on compact Riemann surfaces. - On the Riemann-Roch theorem on compact Riemann surfaces.

2025-08-12 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Robust Sparsification for Matroid Intersection with Applications

by Chien-Chung Huang(CNRS, DI ENS, PSL)

The matroid intersection problem is a fundamental problem in combinatorial optimization. In this problem we are given two matroids and the goal is to find the largest common independent set in both matroids. This problem was introduced and solved by Edmonds in the 70s. The importance of matroid intersection stems from the large variety of combinatorial optimization problems it captures; well-known examples in computer science include bipartite matching and packing of spanning trees/arborescences. In this talk, we introduce a “sparsifer” for the matroid intersection problem and use it to design algorithms for two problems closely related to streaming: a one-way communication protocol and a streaming algorithm in the random-order streaming model. This is a joint-work with François Sellier.

2025-08-18 / 16:00 ~ 17:00

편미분방정식 통합연구실 세미나 - 편미분방정식: Touching vortex dipoles in 2D Euler flows

by ()

Vortex dipoles are one of the most iconic structures in two-dimensional incompressible flows. In this talk, I will present recent results on the existence and stability of traveling wave solutions to the two-dimensional incompressible Euler equations. These solutions take the form of counter-rotating vortex dipoles symmetric across a horizontal axis. A classical example is the Chaplygin–Lamb dipole, where the two vortex regions are tightly packed near the symmetry axis, leading to intense interaction. I will describe a variational framework for constructing such solutions and discuss their dynamical properties. This is joint work with Kyudong Choi and Young-Jin Sim (UNIST).

2025-08-14 / 14:00 ~ 16:00

학과 세미나/콜로퀴엄 - Topology, Geometry, and Data Analysis: Topological Data Analysis with two applications: Tumor Microenvironment and D Chromatography with High-Resolution Mass Spectrometry

by 한주영(Czech Technical University in Prague, 소프트웨어 공학과)

Topological Data Analysis (TDA) has emerged as a powerful framework for uncovering meaningful structure in high-dimensional, complex datasets. In this talk, we present two applications of TDA in analyzing patterns, one in the tumor microenvironment (TME) and the other in high-resolution chemical profiling. In the first case, we develop a TDA-based framework to quantify malignant-immune cell interactions in Diffuse Large B Cell Lymphoma using multiplex immunofluorescence imaging. By introducing Topological Malignant Clusters (TopMC) and leveraging persistence diagrams, we capture both global infiltration patterns and local density-based features. This robust approach enables consistent prognostic assessment regardless of tumor region heterogeneity and reveals correlations with patient survival. In the second application, we utilize the Ball Mapper algorithm to simplify and visualize high-dimensional data obtained from 2D Chromatography with high-resolution mass spectrometry. This enables interpretable chemical profiling of complex mixtures and supports tasks such as sample authentication and environmental analysis. Together, these studies demonstrate the versatility and interpretability of TDA for extracting biologically and chemically meaningful information.

Events for the 취소된 행사 포함