Friday, March 21, 2025

2025-03-21 / 10:00 ~ 11:30

by 이호민()

In this talk, we will discuss about smooth random dynamical systems and group actions on surfaces. Random dynamical systems, especially understanding stationary measures, can play an important role to understand group actions. For instance, when a group action on torus is given by toral automorphisms, using random dynamics, Benoist-Quint classified all orbit closures. In this talk, we will study non-linear actions on surfaces using random dynamics. We will discuss about absolutely continuity and exact dimensionality of stationary measures as well as classification of orbit closures. This talk will be mostly about the ongoing joint work with Aaron Brown, Davi Obata, and Yuping Ruan.

2025-03-25 / 16:00 ~ 17:00

SAARC 세미나 - SAARC 세미나:

by 김동한(KAIST 수리과학과)

H. Föllmer introduced in 1981 a version of Itô's formula without any probabilistic assumptions. It has been generalized in several aspects, including pathwise Tanaka's formula, high-order, and functional change-of-variable formula. Its drawbacks and a brief application to mathematical finance will also be presented.

2025-03-26 / 10:00 ~ 11:00

학과 세미나/콜로퀴엄 - 위상수학 세미나:

by 서동균(서울대학교)

A surface can be decomposed into a union of pairs of pants, a construction known as a pants decomposition. This fundamental observation reveals many important properties of surfaces. By forming a simplicial graph whose vertices represent pants decompositions, connecting two vertices with an edge whenever the corresponding decompositions differ by a simple move, we obtain a graph that is quasi-isometric to the Weil–Petersson metric on Teichmüller space. Meanwhile, topologists often study a structure called a rose, formed by attaching multiple circles at a single point. A rose is homotopy equivalent to a compact surface with boundary. Consequently, we can define a pants decomposition of a rose as the pants decomposition of a surface homotopy equivalent to it. In this talk, we will explore the concept of pants decompositions specifically in the context of roses.

2025-03-27 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄:

by 허영미(연세대학교 수학과)

Wavelets provide a versatile framework for signal representation and analysis, integrating ideas from harmonic analysis, approximation theory, and practical algorithm design. In this talk, we introduce foundational concepts in wavelet theory, focusing on classical results regarding wavelet expansions and approximations. Building on these basics, we explore modern developments and discuss how these approaches can balance theoretical rigor with practical convenience. The presentation aims to offer both a solid introduction to classical wavelet theory and a glimpse into current and future research directions. Part of the talk is based on joint work with Hyojae Lim.

2025-03-28 / 11:00 ~ 12:00

IBS-KAIST 세미나 - IBS-KAIST 세미나:

by ()

Individual human cancer cells often show different responses to the same treatment. In this talk I will share the quantitative experimental approaches my lab has developed for studying the fate and behavior of human cells at the single-cell level. I will focus on the tumor suppressor protein p53, a transcription factor controlling genomic integrity and cell survival. In the last several years we have established the dynamics of p53 (changes in its levels over time) as an important mechanism controlling gene expression and guiding cellular outcomes. I will present recent studies from the lab demonstrating how studying p53 dynamics in response to radiation and chemotherapy in single cells can guide the design and schedule of combinatorial therapy, and how the p53 oscillator can be used to study the principles and function of entertainment in Biology. I will also present new findings suggesting that p53’s post-translational modification state is altered between its first and second pulses of expression, and the effects these have on gene expression programs over time.

2025-03-21 / 11:00 ~ 12:00

IBS-KAIST 세미나 - IBS-KAIST 세미나:

by ()

Our present healthcare system focuses on treating people when they are ill rather than keeping them healthy. We have been using big data and remote monitoring approaches to monitor people while they are healthy to keep them that way and detect disease at its earliest moment presymptomatically. We use advanced multiomics technologies (genomics, immunomics, transcriptomics, proteomics, metabolomics, microbiomics) as well as wearables and microsampling for actively monitoring health. Following a group of 109 individuals for over 13 years revealed numerous major health discoveries covering cardiovascular disease, oncology, metabolic health and infectious disease. We have also found that individuals have distinct aging patterns that can be measured in an actionable period of time. Finally, we have used wearable devices for early detection of infectious disease, including COVID-19 as well as microsampling for monitoring and improving lifestyle. We believe that advanced technologies have the potential to transform healthcare and keep people healthy.

2025-03-24 / 16:00 ~ 17:30

편미분방정식 통합연구실 세미나 - 편미분방정식:

by 김태규()

In this note, we investigate threshold conditions for global well-posedness and finite-time blow-up of solutions to the focusing cubic nonlinear Klein–Gordon equation (NLKG) on $\bbR^{1+3}$ and the focusing cubic nonlinear Schrödinger equation (NLS) on $\bbR$. Our approach is based on the Payne–Sattinger theory, which identifies invariant sets through energy functionals and conserved quantities. For NLKG, we review the Payne–Sattinger theory to establish a sharp dichotomy between global existence and blow-up. For NLS, we apply this theory with a scaling argument to construct scale-invariant thresholds, replacing the standard mass-energy conditions with a $\dot{H}^{\frac12}$-critical functional. This unified framework provides a natural derivation of global behavior thresholds for both equations.

Events for the 취소된 행사 포함