The Bowen Lectures

The Bowen Lectures are supported by anonymous donors, one of whom was an undergraduate student of Rufus Bowen.

The 2018-2019 Bowen Lectures will be given by James McKernan of University of California, San Diego and Christopher Hacon of University of Utah on February 19, 20 and 21, 2019. Each lecture begins at 4:10pm and ends at 5:00pm.

Series Title: Geometry of Algebraic Varieties


Tuesday February 19th
Lecture 1: Symmetries of polynomial equations.
Banatao Auditorium, Sutardja Dai Hall


The symmetries of systems of polynomial equations can be be understood in terms of the geometry of the variety of zeroes (or solution set) of the polynomials. Roughly speaking, there are 3 kinds of geometries corresponding to positive, zero and negative curvature giving rise to 3 different kinds of symmetry groups. In this lecture, I will discuss recent advances in algebraic geometry that lead to very precise results on the structure of these symmetry groups.

Slides of Lecture 1


Wednesday February 20th
Lecture 2: On the birational classification of algebraic varieties.
Banatao Auditorium, Sutardja Dai Hall


Algebraic varieties are geometric objects defined by polynomial equations. The minimal model program (MMP) is an ambitious program that aims to classify algebraic varieties. According to the MMP, there are 3 building blocks: Fano varieties, Calabi-Yau varieties and varieties of general type which are higher dimensional analogs of Riemann Surfaces of genus 0,1 or at least 2 respectively. In this talk I will recall the general features of the MMP and discuss recent advances in our understanding of Fano varieties and varieties of general type.

Slides of Lecture 2


Thursday February 21st
Lecture 3: Birational geometry in characteristic $p>0$.
60 Evans Hall


After recent spectacular progress in the classification of varieties over an algebraic closed field of characteristic 0 (e.g. the solution set of a system of polynomial equations defined by $p_1,...,p_r$ in $C[x_1,...,x_n]$) it is natural to try and understand the geometry of varieties defined over an algebraically closed field of characteristic $p>0$. Many technical difficulties arise in this context. Nevertheless, there has been much progress recently. In particular, the MMP was established for 3-folds in characteristic $p>5$ by work of Birkar, Hacon, Xu and others. In this talk, we will explain some of the challenges and the recent progress in this active area of research.

Slides of Lecture 3


Biographies of Speakers:

Christopher Hacon was born in Manchester, UK but grew up in Pisa, Italy where he attended the Scuola Normale Superiore di Pisa and the University of Pisa. He received his PhD from UCLA in 1998 under the direction of Robert Lazarsfeld. He is currently a distinguished professor at the University of Utah. He is a member the American Academy of Arts and Sciences and the National Academy of Sciences. He is also a recipient of the Clay, Cole and Breakthrough prizes.


James McKernan was born in London, UK. He went to Trinity College in Cambridge, where he obtained a BA in mathematics and then took Part III. He first went to Brown and then transferred to Harvard where he obtained his PhD under the direction of Joe Harris. He is currently a professor at the University of San Diego. He is a Fellow of the Royal Society and a recipient of the Clay, Cole and Breakthrough



Born in 1947 in Vallejo, California, Robert Edward (Rufus) Bowen was awarded the AB with prizes for scholarship by the University of California at Berkeley in 1967. His doctorate in Mathematics was completed in Berkeley in 1970 under the direction of Stephen Smale. In that year he was appointed to the faculty of the Department of Mathematics at Berkeley. He was promoted to the rank of Professor in 1977.

Bowen worked in mathematical dynamics systems theory. His pioneering studies of topological entropy, symbolic dynamics, Markov partitions, and invariant measures are of lasting importance; much of today's research is inspired by his ideas.

Past Bowen Lecturers

1981-82     Dennis Sullivan
1982-83     Anatol Katok
1983-84     Michael Atiyah
1984-85     John Franks
1985-86     William Parry
1986-87     Nancy Kopell
1987-88     Blaine Lawson
1988-89     David Ruelle
1989-90     Yuri Manin
1990-91     John Milnor
1991-92     Philip Holmes
1992-93     Israel M. Gelfand
1993-94     Alain Connes
1994-95     Shing-Tung Yau
1995-96     Peter Sarnak
1996-97     Vladimir Arnold
1997-98     Simon Donaldson
1998-99     Barry Mazur
1999-00     Cliff Taubes
2000-01     Don Zagier
2001-02     Yakov G. Sinai
2002-03     Roger Penrose
2003-04     Richard Hamilton
2004-05     Curt McMullen
2005-06     John Conway
2006-07     Edward Witten
2007-08     Michael Freedman
2008-09     Hillel Furstenberg
2009-10     Christophe Soulé
2010-11     Michael Hopkins
2011-12     Cédric Villani
2012-13     Benedict Gross
2013-14     Jeff Cheeger
2014-15     Dusa McDuff
2015-16     Jacob Lurie
2016-17     Michael Harris
2017-18     Avi Wigderson