The Bowen Lectures

Rufus BowenBorn 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.

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


The 2021 Bowen Lectures will be delivered by Richard Kenyon, Yale University.

Each lecture starts at 4:10 p.m. and ends at 5:00 p.m. in Lewis Hall Room 100

Title of the Series: Multinomial random tilings and other models.
Series Overview:
This is joint work with Cosmin Pohoata. Random tiling models are an important subarea of combinatorics, probability and statistical mechanics. Typically, however, they are quite difficult to analyze. We define a variant of the random tiling model, the "multinomial random tiling model" which is much easier to study. We find explicit and diverse behavior including phase transitions, crystallization and quasicrystallization, and conformal invariance. We can also define multinomial versions of other stat mech models such as the Ising or Potts model; these can be effectively analyzed on essentially arbitrary graphs, in contrast to standard versions of these models which are NP hard on most graphs.

Tuesday, October 5, 4:10-5 PM Lewis Hall Room 100.
Lecture 1: Multinomial random tilings.
Abstract:
We give definitions and combinatorial results. We relate the model to a certain high-dimensional random walk. We study the special case of multinomial “domino tilings” and its limit shapes.

Wednesday, October 6, 4:10-5 PM Lewis Hall Room 100.
Lecture 2: Fluctuations and conformal invariance.
Abstract
:
We study the fluctuations of the tile densities in the model, showing that they are Gaussian and giving an explicit description of their covariance function. We study multinomial tilings in the plane with various sets of polyominos such as the L polyomino. We describe the associated crystals, quasicrystals and Gaussian scaling limits.

Friday, October 8 4:10-5 PM Lewis Hall Room 100.
Lecture 3: The multinomial Ising and Potts model
Abstract
:
We define the models, compute the various critical temperatures on an arbitrary graph, and describe the fluctuations. We also describe the limit shapes in 1d and of the “Ising droplet” on Z^2.

Biography of Speaker:

Richard KenyonRichard Kenyon received his Ph.D. from Princeton University in 1990 under the direction of William Thurston. After a postdoc at IHES, he held positions at CNRS in Grenoble, Lyon, and Orsay and then became professor at UBC, Brown University and then Yale where he is currently Erastus L. Deforest Professor of Mathematics. He was awarded the CNRS bronze medal, the Rollo Davidson prize, the Loève prize, is a member of the American Academy of Arts and Sciences, and is a Simons Investigator.

Past Bowen Lecturers

2021-22 Richard Kenyon
2020-21 Efim Zelmanov
2018-19 James McKernan and Christopher Hacon
2017-18 Avi Wigderson
2016-17 Michael Harris
2015-16 Jacob Lurie
2014-15 Dusa McDuff
2013-14 Jeff Cheeger
2012-13 Benedict Gross
2011-12 Cédric Villani
2010-11 Michael Hopkins
2009-10 Christophe Soulé
2008-09 Hillel Furstenberg
2007-08 Michael Freedman
2006-07 Edward Witten
2005-06 John Conway
2004-05 Curt McMullen
2003-04 Richard Hamilton
2002-03 Roger Penrose
2001-02 Yakov G. Sinai
2000-01 Don Zagier
1999-00 Cliff Taubes
1998-99 Barry Mazur
1997-98 Simon Donaldson
1996-97 Vladimir Arnold
1995-96 Peter Sarnak
1994-95 Shing-Tung Yau
1993-94 Alain Connes
1992-93 Israel M. Gelfand
1991-92 Philip Holmes
1990-91 John Milnor
1989-90 Yuri Manin
1988-89 David Ruelle
1987-88 Blaine Lawson
1986-87 Nancy Kopell
1985-86 William Parry
1984-85 John Franks
1983-84 Michael Atiyah
1982-83 Anatol Katok
1981-82 Dennis Sullivan