主讲人：何塞·施雅德教授

日期: 2023年5月8日（星期一）

时间：上午9:45-11:15

地点：行政楼西翼W201会议室

语言：英文

Topic: Invariants of flows on singular spaces

Speaker: Prof. José A. Seade

Date: May 8, 2023 (Monday)

Time: 9:45 a.m.-11:15 a.m.

Venue: Room W201, West Wing, Administration Building

Language: English

嘉宾简介

José A. Seade

何塞·施雅德教授于1977年和1980年获得了牛津大学的硕士和博士学位，此后一直于墨西哥国立自治大学（UNAM）数学研究所任研究职位。施雅德教授的主要研究领域为动力系统和奇点理论，在全球范围内享有盛誉。他曾受邀在世界顶级研究机构担任教职，如牛津、巴黎和香港大学，法国里昂的法国高等师范学校，以及印度的塔塔基础研究所。他曾在意大利的国际理论物理中心（ICTP）担任研究员，现正在清华丘成桐数学科学中心进行访问。

何塞·施雅德教授在顶尖杂志上发表了众多论文，包括《Inventiones Mathematicae》、《Journal of Differential Geometry》、《Topology》、《Mathematische Annalen》以及《Advances in Mathematics》等，并已在知名出版社发表了三部研究专著。此外，他现正负责协调出版《奇点的几何与拓扑手册》，该手册共分六卷，由奇点理论领域的86位世界领导者撰写。2021年，他荣获美洲数学委员会颁发的所罗门·莱夫谢茨奖章，并在2005年及2012年两次获得西班牙费兰·苏尼尔·巴拉圭数学奖。

施雅德教授是发展中国家科学院（TWAS，也称“世界科学院”）院士、班夫国际数学创新与探索研究站（BIRS）董事会成员、太平洋数学科学研究所（PIMS）成员以及拉丁美洲和加勒比数学家联盟（UMALCA）成员。他还曾任法国国家科学研究中心（CNRS）在墨西哥的国际研究实验室主任（2009-2022）以及墨西哥瓦哈卡数学之家主任（2017-2023），后者是BIRS的墨西哥分会。此外，施雅德教授还曾担任墨西哥数学学会主席（1986-1988年）和墨西哥国立自治大学（UNAM）数学研究所主任（2014-2022年）。他现担任墨西哥国家科学院副主席以及当选主席（2023-2026年）。

He got his master’s and Ph. D. degrees from the University of Oxford in 1977 and 1980 respectively, and ever since he has held a research position at the Mathematics Institute of Universidad Nacional Autónoma de México (UNAM). His main areas of research are dynamical systems and singularity theory, areas in which he is well-known world-wide. He has been an invited professor at several of the most distinguished research institutions in the world, as for instance the universities of Oxford, Paris and Hong Kong, at the École Normal Superieure of Lyon, France, at the Tata Institute of Fundamental Research in India. He was a Staff Associate at the International Center for Theoretical Physics (ICTP) in Trieste, Italy, and he is now visiting the Yau Mathematical Center at Tsinghua University.

José Seade has several papers published in top journals, such as Inventiones Mathematicae, Journal of Differential Geometry, Topology, Mathematische Annalen, Advances in Mathematics, and others, and he has published three research monographs in distinguished editorial houses. Also, he is now coordinating the publication of the handbook of Geometry and Topology of Singularities, a collection of six volumes with contributions by 86 of the world-leaders in singularity theory. In 2021 he was awarded the Solomon Lefschetz Medal by the Mathematical Council of the Americas, and he has been awarded twice the Ferran Sunyer I Ballaguer Prize (Spain), in 2005 and 2012.

He is a Member of the World Academy of Sciences (TWAS). He has been a member of the Board of the Banff International Research Station (BIRS), of the Pacific Institute for the Mathematical Sciences (PIMS) and of the Latin American and the Caribbean Union of Mathematicians (UMALCA). Also, he was director of a France CNRS International Research Laboratory in Mexico (2009-2022), and of Casa Matemática Oaxaca (2017-2023), a BIRS Affiliate in Mexico. He was President of the Mexican Mathematical Society (1986-1988) and Director of UNAM’s Mathematics Institute for two periods (2014-2022). He currently is Vice-President of the Mexican Academy of Sciences and Elected President of that Academy for the period 2023-2026.

摘要 Abstract

流现象在许多科学领域中均有出现。在天体力学等学科中，流代表的是运动。流的定义方式有多种，其中之一是通过向量场：在每个点处，向量告诉我们移动的方向，以及以移动速度的大小。静止点或固定点是流研究的基石之一，它们对应于向量场的零点（或相应微分方程的常数解）。此类点的一个重要不变量为局部庞加莱—霍普夫指标。关于该指标及其推广的研究文献非常丰富。在本次讲座中，我们将深入介绍这个主题，并探讨环绕空间变得不再光滑、而是一个奇异流形（如轨形）的情形。

Flows appear in most areas of science. These represent movement, as for instance in Celestial Mechanics. Flows can be defined in various ways, one of these is by means of vector fields: at each point, the vector tells us in which direction we must move, and at which speed. A cornerstone when studying flows is the stationary or fixed points; these correspond to zeros of the vector field (or constant solutions of the corresponding differential equation). And a basic invariant of such points is the local Poincaré-Hopf index. The literature about this index and its generalizations is vast. We will give an introduction to this topic and look at the case where the ambient space is no longer smooth but a singular variety, as for instance an orbifold.