# The Bowen Lectures

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

**The 2017-2018 Bowen Lectures** will be given by Avi Wigderson of the Institute for Advanced Study, on February 7, 8 and 9, 2018. Each lecture begins at 4:10pm and ends at 5:00pm.

Series Title: **Mathematics and Computation (through the lens of one problem and one algorithm)**

Wednesday February 7th

Lecture 1: *The problem, the algorithm and the connections.*

Calvin Laboratory (Simons Institute) Auditorium

Thursday February 8th

Lecture 2: *Proving Algebraic Identities.*

60 Evans Hall

Friday February 9th

Lecture 3: *Proving Analytic Inequalities.*

Calvin Laboratory (Simons Institute) Auditorium

Series Abstract:

Mathematics and computation have gone hand in hand for millennia. Many of the greatest mathematicians we great algorithm designers as well, including Euclid, Newton, Gauss and Hilbert. And since the creation of the theories of computation and then computational complexity, these connections have become far broader, deeper and stronger.

This 3-lecture series will illustrate these connections by focusing on a single computational problem, Singularity of Symbolic Matrices, and a single algorithmic technique for it, Alternate Minimization. As it happens, recent attempts to understand these have uncovered a surprisingly rich web of connections between diverse areas of mathematics and computer science, all of which contributing and benefitting from this interaction. In math these include non-commutative algebra, invariant theory, quantum information theory and analysis. In computer science they include optimization, algebraic complexity and pseudorandomness.

In this first lecture I will give the general set-up, motivating and explaining the problem, algorithm and main results, as well as some of the connections.

In the next two lectures I will survey aspects of two central problems to both math and CS, Proving Algebraic Identities and Proving Analytic Inequalities, motivating and influenced by the research above.

While very related, all three lectures are designed to be independent of each other. They require no special background knowledge.

Lecture notes for much of this material can be found in http://www.math.ias.edu/~avi/PUBLICATIONS/CCC-17-tutorial-lecture-notes.pdf

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