2016清华大学陈省身讲座
报告人：Fernando Marques，普林斯顿大学
时间：10:30-11:30，5月10日（周二），12日（周四）
地点：清华大学近春园西楼三层报告厅
报告人简介
Fernando Codá dos Santos Cavalcanti Marques，巴西数学家，普林斯顿大学教授，主要研究领域是几何，拓扑和偏微分方程。2012年，他和André Neves一起解决了Willmore猜想。
Fernando Marques于2003年在康奈尔大学获得博士学位，师从José Fernando Escobar。2003年至2014年，他任职于IMPA。2014年9月1日，他入职普林斯顿大学担任教授。
他的部分著名成果如下：
与André Neves合作解决Willmore猜想。他与Neves合作的论文“Min-max theory and the Willmore conjectur”于2012年2月上传至arXiv，在这篇论文中，他们使用Almgren–Pitts极大极小定理解决了Willmore猜想。
2012年，与Ian Agol和André Neves合作解决了Freedman–He–Wang猜想。
2010年，与Simon Brendle and André Neves合作提出Min-Oo刚性猜想的一个反例。
Marques教授在2010年的国际数学家大会上做45分钟报告，在2014年的国际数学家大会上做一小时报告。他在2012年获得国际理论物理中心拉马努金奖，并在2016年和André Neves同获维布伦几何奖。2014年，Marques教授当选为巴西科学院院士。
2016 Tsinghua University Shiing-Shen Chern Distinguished Lecture
Speaker: Fernando Marques [Princeton University]
Time: 10:30-11:30, May 10 (Tue.), May 12 ( Thu.)
Place: Lecture Hall, Floor 3, Jin Chun Yuan West Building, Tsinghua University
Title: "Min-max theory for the area functional - a panorama"
Abstract:
In these lectures we will give a current panorama of the min-max theory for the area functional, initially devised by Almgren in the 1960s and improved by Pitts (1981). This is a deep high-dimensional generalization of the study of closed geodesics. The setting is very general, being that of Geometric Measure Theory, and the main application until very recently was the construction of minimal varieties of any dimension in a compact Riemannian manifold.
In the past few years we have discovered new applications of this old theory, including a proof of the Willmore conjecture, of the Freedman-He-Wang conjecture, and of Yau's conjecture (about the existence of infinitely many minimal hypersurfaces) in the positive Ricci curvature setting. We will give an overview of these results, describe our current efforts to develop the theory further and discuss future directions. Among the most recent developments, we will describe our work on the problems of the Morse index and multiplicity of min-max minimal hypersurfaces. Most of the material covered in these lectures is based on joint work with Andre Neves.
Introduction of Speaker
Fernando Codá dos Santos Cavalcanti Marques is a Brazilian mathematician working mainly in geometry, topology and partial differential equations. He is a professor at Princeton University. In 2012, together with André Neves, he proved the Willmore conjecture.
Fernando Marques obtained his Ph.D. from Cornell University in 2003, under the supervision of José Fernando Escobar. He worked at the IMPA from 2003 to 2014. On September 1, 2014, Marques joined Princeton University as a full professor.
Some of his best known works are the following:
In cooperation with André Neves, the solution to the Willmore conjecture (2012). Marques and Neves "Min-max theory and the Willmore conjecture" was uploaded to arXiv on February 2012, in it they solved the Willmore conjecture, using Almgren–Pitts min-max theory.
In cooperation with Ian Agol and André Neves, the solution to the Freedman–He–Wang conjecture (2012)
In cooperation with Simon Brendle and André Neves, a counter-example to the rigidity conjecture of Min-Oo (2010)
He was an invited speaker at the International Congress of Mathematicians (ICM) of 2010 in Hyderabad, and a plenary speaker at the ICM of 2014 in Seoul. He was awarded the ICTP Ramanujan Prize in 2012. He is a member of the Brazilian Academy of Sciences since 2014. He shared the 2016 Oswald Veblen Prize in Geometry with André Neves.
|
