[Distinguished Lecture] On the Topology of a Holomorphic Map Near a Critical Point
Speaker(s): Jose Seade (National University of Mexico and Mexican Academy of Sciences)
Time: 16:00-17:00 February 17, 2025
Venue: Lecture Hall, Jiayibing Building, Jingchunyuan 82, BICMR
Let $U$ be an open neighborhood of Let $U$ be an open neighborhood of $\underline 0$ in $\mathbb{C}^m$ and $f: (U, \underline 0) \to (\mathbb{C},0)$ holomorphic with a critical point at $\underline 0$; set $V = f^{-1}(0)$. Then $V$ is an analytic variety with a possibly non-isolated singularity at $\underline 0$. A classical way to study the geometry and topology of $V$ is by looking at a local non-critical level $F_t$, known as the Milnor fiber. And an also classical way to study the topology of $F_t$ is by slicing it with the level surfaces $\ell^{-1}(s)$ of some general linear form $\ell$; or more generally with the level surfaces of another holomorphic function $g$ which is “good” with respect to $f$. This goes back to ideas of Thom in the 1960s and developed further by Lê Dũng Tráng, Teissier and others. In particular one has the celebrated Lê-Greuel formula for the Milnor number.(s) of some general linear form ℓ; or more generally with the level surfaces of another holomorphic function $g$ which is “good” with respect to $f$. This goes back to ideas of Thom in the 1960s and developed further by Lê Dũng Tráng, Teissier and others. In particular one has the celebrated Lê-Greuel formula for the Milnor number.
In this talk we will revise these results and explain how to generalize these to functions on varieties with arbitrary singular locus.This is recent work with Lê Dũng Tráng and J. Nuño-Ballesteros.
报告人简介：
Jose Seade 教授于1976年获得墨西哥国立自治大学（UNAM）数学学士学位，并分别于1977年和1980年获得英国牛津大学硕士学位和博士学位。自1980年以来，他一直在墨西哥国立自治大学数学研究所工作。自1985 年起成为墨西哥科学院成员，自 2003 年起成为世界科学院 (TWAS) 成员。
他的研究兴趣包括奇点理论、动力系统和复几何，在这些领域发表了近 100 篇研究文章和书籍，被公认为世界权威。
他曾两次荣获 Ferran Sunyer i Balaguer(费兰·桑耶·巴拉格) 奖（2005 年和 2012 年），并于 2021 年获得了所罗门·莱夫谢茨奖章（Solomon Lefschetz Medal），该奖章由美洲数学委员会每四年颁发一次。他担任墨西哥数学会主席（1986-1987）并创立了墨西哥数学奥林匹克竞赛。他还在墨西哥库埃纳瓦卡创立了所罗门·莱夫谢茨国际数学实验室，该实验室与法国国家科学研究中心有联系，并于 2009 年至 2022 年担任该实验室主任。他是拉丁美洲和加勒比数学联盟 （UMALCA ）科学委员会成员（2001-2009 年），并担任联盟执行委员会成员直至 2017 年。他从2017年 1 月至2023年1月担任瓦哈卡数学之家主席，2014年至2022年两期担任墨西哥国立自治大学数学研究所所长。
