The Bowen Lectures

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

The 2016-2017 Bowen Lectures will be given by Michael Harris of Columbia University, on February 22, 23 and 24, 2017. Each lecture begins at 4:10pm and ends at 5:00pm.

Series Title: Automorphic Galois representations and Langlands correspondences

Series Abstract:

The Langlands program can be seen as a framework for using sophisticated methods of analysis, geometry, and group theory to derive insights into fundamental questions of number theory, specifically the structure of Galois groups of polynomial equations with rational coefficients. It can also be seen as a way to use Galois theory to find some order in the infinite-dimensional representation theory of important classes of topological groups, including semisimple Lie groups and their p-adic counterparts. The past few years has seen spectacular progress in both perspectives, thanks in large part to new ideas introduced by Peter Scholze and Vincent Lafforgue, based on p-adic geometry and geometric representation theory. The lecture series will introduce some of the goals of the Langlands program, and will review how much closer we are to achieving them than we were a few years ago, and how much remains to be accomplished.



Wednesday February 22, 2017
Lecture 1: Galois representations and automorphic forms: an introduction to the Langlands program
Room 50, Birge Hall

Automorphic forms are functions on a class of homogeneous spaces that arise naturally naturally in geometry and number theory and that enjoy particularly strong symmetry properties (the simplest non-trivial example is the circle). Galois representations are efficient ways of packaging meaningful information about solutions to polynomial equations; the cohomology of algebraic varieties provides a rich supply of such packages. The Langlands program is predicated on the insight that these two branches of mathematics are to a large extent about the same thing.



Thursday February 23, 2017
Lecture 2: Attaching Galois representations to automorphic forms, and vice versa: recent progress
Room 60, Evans Hall

Most of the Galois representations whose properties can be studied are obtained by analyzing the cohomology of Shimura varieties, and of the moduli spaces (stacks) of shtukas, which are families of vector bundles over curves over finite fields with extra structure. This lecture reports on recent work on these automorphic Galois representations, with an emphasis on the contributions of Scholze and V. Lafforgue.



Friday February 24, 2017
Lecture 3: An idiosyncratic survey of open problems
Room 740, Evans Hall

The final lecture will focus on a few questions in the Langlands program that may be on the verge of solution, and on other questions that at present appear completely out of reach.



 

 

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