# 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 first series of Chern Lecturers in 2022-23 will be given by Professor Peter Sarnak**, Professor, Princeton University and Institute for Advanced Study (January 31st, February 2nd, February 7th, and February 9th, 2023). The title of the series is "Spectra of locally uniform geometries".

**Lecture 1 of 4 **(Jan-31-2023 @ 4:10–5:00 pm, UC Berkeley Campus, Location TBD)**: **Spectra of Locally Uniform Geometries: Prescribing the spectrum --- Locally symmetric Riemannian spaces. ABSTRACT: We review recent developments (conformal bootstrap and random covers) concerning the bass-note of the spectrum of Laplacians on hyperbolic manifolds and on large cubic graphs. We highlight rigidity to creating spectral gaps when restricting the geometries. Lecture 1 will focus on locally symmetric Riemannian spaces.

**Lecture 2 of 4: **(Feb-02-2023 @ 4:10–5:00 pm, 60 Evans Hall): Spectra of Locally Uniform Geometries: Prescribing the spectrum --- Cubic graphs. ABSTRACT: We review recent developments (conformal bootstrap and random covers) concerning the bass-note of the spectrum of Laplacians on hyperbolic manifolds and on large cubic graphs. We highlight rigidity to creating spectral gaps when restricting the geometries. Lecture 2 will focus on cubic-graphs and the eigenvalues of Frobenius for curves and abelian varieties. Joint work with Alicia Kollar and Fan Wei. *Note: This lecture will be taking place as part of the Department of Mathematics' Spring '23 Colloquium Series.*** **

**Lecture 3 of 4** (Feb-07-2023 @ 4:10–5:00 pm, UC Berkeley Campus, Location TBD): Spectra of Locally Uniform Geometries: The additive structure of the spectrum of a metric graph. ABSTRACT: Metric graphs are compact one dimensional Riemannian manifolds with singularities and have been studied in different guises. Using tools from diophantine analysis we determine the additive and transcendence properties of their spectra and its applications to crystalline measures. Joint work with Pavel Kurasov.

**Lecture 4 of 4: **(Feb-09-2023 @ 4:10-5:00 pm, UC Berkeley Campus, Location TBD): Spectra of Locally Uniform Geometries: The general Ramanujan. and density conjectures. ABSTRACT: The naive extension of Satake's formulation of the Ramanujan conjectures fails in any generality. Arthur's conjectures are a far reaching remedy but they remain largely out of reach. After reviewing these briefly we describe a simple density conjecture which serves as complete substitute for various applications and which has been proven recently in many cases.

### 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 Yako Eliashberg