# The Bowen Lectures

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.

*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**. The **Zoom** link for all meetings is https://berkeley.zoom.us/j/91863998034.

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**.*Zoom link*: https://berkeley.zoom.us/j/91863998034

*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**.

* Zoom link: https://berkeley.zoom.us/j/91863998034Abstract*:

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**.

* Zoom link: https://berkeley.zoom.us/j/91863998034Abstract*:

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 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

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

2018-19 James McKernan and Christopher Hacon

2020-21 Efim Zelmanov