# 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: https://senate.universityofcalifornia.edu/_files/inmemoriam/html/shiingshenchern.htm

The Department of Mathematics will host the **2023-24 Chern Lecture **during the Fall '23 semester: Professor Bernd Ulrich of Purdue University will be the speaker.

**Speaker: ****Bernd Ulrich **(Purdue University)

November 7, 8, 9

**Title of the series**: **Equisingularity, linkage, and the implicitization problem**

This is a series of independent talks on three topics where algebra, singularity theory, and algebraic geometry come together.

**Lecture 1:** Tuesday, November 7, 4:10-5 pm, 102 Moffitt Library

**Title**: **Equisingularity and multiplicities.**

A goal in equisingularity theory is to devise criteria for analytic sets to be "alike," especially when they occur in a family. Ideally, such criteria only depend on numerical invariants of the individual members rather than the total space of the family. It was Teissier's seminal insight to relate the known equisingularity conditions, such as the geometric conditions of a Whitney stratification, to the algebraic concept of multiplicity. Thus he was able to characterize the equisingularity of families of isolated hypersurface singularities. Any generalization beyond the case of isolated hypersurface singularities however, requires new notions of multiplicities. The talk will survey past and present work on this subject and explain the connection with multiplicity theory.

Reception to follow in 1015 Evans

**Lecture 2. **Wednesday, Nov 8, 4:10-5 pm, 180 Tan Hall

**Title: Linkage of algebraic varieties and ideals.**

Linkage, or liaison, is a tool for classifying and studying varieties, ideals, and algebras. The theory has its origins in the nineteenth century, and it was recast in modern algebraic language and studied extensively since the 1970s. In this talk we will introduce the subject and lead up to more recent work on a generalization of linkage that arises naturally in intersection theory.

**Lecture 3.** Thursday, Nov 9, 4:10-5 pm, 60 Evans Hall

**Title: The implicitization problem for algebraic varieties. **

The talk is concerned with a classical problem in elimination theory that has also been of interest in applied mathematics -- the problem of determining the equations of a variety that is given parametrically. A wide range of tools has been developed for this question, and we will describe some of them. We will also explain how knowing the types of singularities of a variety can inform the search for its implicit equations.

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**Bernd Ulrich** received his doctoral degree in 1980 from the University of the Saarland in Germany. He became a Professor of Mathematics at Michigan State University in 1986 and moved to Purdue University in 2001. He spent three semesters at MSRI, where he held a Research Professorship in 2012/13, he was a Simons Foundation Fellow in 2013, and he will spend the Spring of 2024 at SLMath as a Clay Senior Scholar. He is a Fellow of the AMS, and he has graduated 25 doctoral students. His work is in commutative algebra and algebraic geometry, with an emphasis on topics in algebra that are motivated by geometry and singularity theory, such as liaison, intersection theory, residual intersection, equisingularity theory, multiplicity theory, and Rees algebras.

### 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

2023-24 Bernd Ulrich