活動時程
13:00-13:30 報到
13:30-14:30 心得經驗分享與綜合座談
14:30-14:45 休息
14:45-15:15 李永丞(課程A. 重點分享)
15:15-15:45 蕭明 (課程A. 重點分享)
15:45-16:00 休息
16:00-16:30 蔡以心(課程B. 重點分享)
16:30-17:00 許嘉麟(課程A. 重點分享)
【Abstract】報告人: 李永丞
K-stability is a algebro-geometric condition that people expect to be equivalent to the existence of extremal metric on Fano varieties. In recent years, there are some researches of K-stability based on non-Archimedean geometry (in the Berkovich sense). I will first introduce the Berkovich geometry, and explain how it relates to the study of K-stability if time permits.
【Abstract】報告人: 蕭明
In this talk, I will summarize key concepts and results from R. Bamler's course, "Ricci Flow with Surgery in Higher Dimensions." First, I will briefly review the classical results in Ricci flow, including Hamilton's and Perelman's groundbreaking work in 3-dim. Next, I will discuss Appleton's example, which illustrates that the singular model may develop singularities in dimensions four and higher. Finally, I will present Bamler's result concerning the characterization of the blow-down limit of the singular model in 4-dim.
【Abstract】報告人: 蔡以心
We will focus on the microlocal analysis part of this summer school, specifically discussing some symbol spaces and pseudodifferential operators. We will begin by exploring Kohn-Nirenberg symbols and analyze the impact of ellipticity on operators and their parametrices. Furthermore, we will extend our discussion to include scattering symbols and b-calculus.
【Abstract】報告人: 許嘉麟
In this talk, we will introduce the level set approach to mean curvature flow of hypersurfaces in Euclidean space. In recent decades, methods for going through singularities of mean curvature flow have been widely studied. Among these methods, by applying the so called avoidance principle, we can establish the theory of level set flow, which can be defined globally for any initial closed subsets. We will discuss its relation to classical solutions and some uniqueness problems. If time permits, we will also cover higher-codimensional mean curvature flow in Euclidean space. The content of this talk is based on lectures by R. Haslhofer at SMS 2024 (Montr´ eal, Canada) and the paper [1] authored by A. Luigi and H. Mete Soner.
References
[1] Luigi Ambrosio and Halil Mete Soner. “Level set approach to mean curvature flow in arbitrary codimension”. In: J. Differential Geom. 43.4 (1996), pp. 693–737. issn: 0022-040X,1945-743X. http:// projecteuclid.org/euclid.jdg/1214458529.
