Wednesday, March 19, 2025

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

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.

2025-03-20 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄:

by 김연수(전남대학교 수학교육과)

TBD

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.

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