# The Chern Lectures

The Shiing-Shen Chern Chair in Mathematics was established by a generous donation by Dr. Robert G. Uomini, a 1976 graduate from UC Berkeley, and Ms. Louise B. Bidwell in honor of one of the 20th century's greatest geometers, Shiing-Shen Chern, Professor Emeritus, UC Berkeley. Funds from the endowment are used to support one or more distinguished visiting mathematicians each year as well as teaching and research activities related to the visitors. The visitors are referred to as The Shiing-Shen Chern Visiting Professors.

**The 2016-2017 Chern Lectures** will be given by Sergiu Klainerman of Princeton University, on January 31 and February 1, 2 and 3, 2017. The title of the series is "On the Mathematical Theory of Black Holes".

**On the Mathematical Theory of Black Holes**

The gravitational waves detected recently by LIGO were produced in the final phase of the inward spiraling of two black holes before they collided to produce a more massive black hole. The experiment is entirely consistent with the so-called Final State Conjecture of general relativity, according to which general solutions of the initial value problem approach asymptotically, in any compact region, a Kerr black hole. Although the conjecture is so very easy to formulate and happens to be validated by both astrophysical observations as well as numerical experiments, it is far beyond our current mathematical understanding, let alone techniques. In fact, even the far simpler and fundamental question of the stability of the Kerr black hole remains wide open.

In my lectures I will address the issue of stability as well as other aspects of the mathematical theory of black holes, such as rigidity of black holes and the problem of collapse. The rigidity conjecture asserts that all stationary solutions of the Einstein vacuum equations must be Kerr black holes, while the problem of collapse addresses the issue of how black holes form in the first place from regular initial conditions. Recent advances on all these problems were made possible by a remarkable combination of novel geometric and analytic techniques, which I will try to outline in my lectures

**Lecture 1:**

Tuesday, January 31, 2017

4:00 pm - 5:00 pm, Banatao Auditorium, 310 Sutardja Dai Hall

On the reality of black holes

Abstract: I will give a quick introduction to the initial value problem in general relativity, along with an overview of the problems of rigidity, stability and collapse, and how they fit with regard to the Final State Conjecture.

*A reception in honor of the speaker will be held following the first lecture at 5:15 pm in 1015 Evans Hall.*

**Lecture 2:**

Wednesday, February 1, 2017

4:00 pm - 5:00 pm, Banatao Auditorium, 310 Sutardja Dai Hall

Rigidity of black holes

**Lecture 3:**

Thursday, February 2, 2017

4:00 pm - 5:00 pm, Room 60, Evans Hall

The problem of stability

**Lecture 4:**

Friday, February 3, 2017

4:00 pm - 5:00 pm, Room 939, Evans Hall

The problem of collapse

Professor Chern (1911-2004) is widely regarded as the greatest geometer of his generation. For more than six decades, he was a leader in the field of differential geometry and made significant contributions to such diverse areas as the geometry of fibre bundles, complex geometry, web geometry, integral geometry, Nevalinna theory, and the classical theory of submanifolds in euclidean space. Professor Chern completed his doctorate in 1936 in Hamburg. During his stay at the Institute for Advanced Study at Princeton in 1943-1945, he did his ground-breaking work on characteristic classes and fibre bundles. When he returned to China in 1946, he set himself the task of introducing modern mathematics to China and succeeded in training a new generation of Chinese mathematicians. Professor Chern taught at the University of Chicago from 1949 to 1960, when he came to Berkeley. He was a co-founder of the Mathematical Sciences Research Institute in Berkeley. He retired in 1979.

Additional biographical information can be found at:

http://www.universityofcalifornia.edu/senate/inmemoriam/shiingshenchern.htm

### Past Chern Visiting Professors

1996 Sir Michael Atiyah

1997 Richard Stanley

1998 Friedrich Hirzebruch

1999 Michael Artin

Yuri Manin

2000 Don Zagier

2001 Joseph Bernstein

Peter Lax

Bertram Kostant

2005 Terence Tao

2007 Vladimir Igorevich Arnold

2008 Dennis Sullivan

2009 Richard Taylor

2010 Peter S. Ozsvath

2011 Andrei Okounkov

2012 Jean Bourgain

2013 (Spring) Nigel Hitchin

2013 (Fall) Stanislav Smirnov

2014 Ngô Bảo Châu

2015-16 Alex Eskin