# 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.

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

The Department of Mathematics will host two **2022-23 Chern Lecturers **during the Spring '23 semester: Professor Peter Sarnak, Professor, Princeton University and Institute for Advanced Study (January-February) and Yakov Eliashberg, Professor, Stanford University (April).

**The second series of Chern Lecturers in 2022-23 will be given by Professor Yakov Eliashberg**, the Herald L. and Caroline L. Ritch Professor of Mathematics at Stanford University (April 18, April 20, April 25, and April 26, 2023). The title of the series is "Flexible Mathematics". The overall abstract for the series is: *Flexible mathematics was born in the work of Hassler Whitney in 1930s-1940s, Stephen Smale and John Nash in 1950s, and then greatly developed by Mikhail Gromov in the late 1960s-early 1970s under the name of the h-principle. In recent years the area went through a period of renaissance. In the lectures there will be discussed the evolution of notions and methods of the h-principle and consider a few recent examples from complex, symplectic and contact geometries. *Please join us for a reception in 1015 Evans after the first lecture on April 18 beginning around 5:15pm.

**Lecture 1 of 4 **(April 18, 2023 @ 4:10–5:00 pm, UC Berkeley Campus, Location: Sibley Auditorium - Bechtel)**: "h-principle and its evolution"**. ABSTRACT: Our understanding which problem belong to the domain of the h-principle has evolved since the inception of the subject. We will explore the development of basic methods and ideas on various examples.

**Lecture 2 of 4: **(April 20, 2023 @ 4:10–5:00 pm, Location: 60 Evans Hall): **"Flavors of convexity in complex geometry"**. ABSTRACT: We will discuss two instances of h-principle in complex geometry and analysis: the Oka principle in the theory of holomorphic functions on Stein manifolds and the theory of complex convexity in its various flavors, such as pseudo-convexity, holomorphic, rational and polynomial convexity. Complex convexity has counterparts in symplectic and contact geometry, and this interplay turned out to be useful for all sides of the story.

**Lecture 3 of 4** (April 25, 2023 @ 4:10–5:00 pm, UC Berkeley Campus, Location: Valley Life Science Building 2060): **"Wienstein manifolds: on the frontier of symplectic flexibility"**. ABSTRACT: In symplectic and contact geometry flexible and rigid results come in a striking proximity. We consider a few examples in the theory of Weinstein manifolds, which are symplectic counterparts of Stein complex manifolds.

**Lecture 4 of 4: **(April 26, 2023 @ 4:10-5:00 pm, UC Berkeley Campus, Location: Valley Life Science Building 2060): **"Convexity in contact geometry"**. ABSTRACT: Recently Ko Honda and Yang Huang discovered a new flexibility phenomenon related to contact convexity. We will discuss their result and some further development in this direction.

### 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

2016-17 Sergiu Klainerman

2017-18 Martin Hairer

2018-19 Assaf Naor

2022-23 Peter Sarnak

2022-23 Yakov Eliashberg