William Thurston Lectures

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2023 Thurston Lectures

The Thurston Lectures are named after Fields Medalist and former UC Davis mathematician William Thurston. The next Thurston Lecture series will be given by Richard Kenyon (Yale University) on May 10-12, 2023.

Series title: Dimers, webs and SL(n) local systems I,II,III

Detailed schedule: To Be Announced

Abstract:
One of Bill Thurston’s many side projects was a result on domino tilings (tilings with 2x1 and 1x2 rectangles): he gave an algorithm for deciding when a planar polygon could be tiled with dominos. The domino tiling model (and more generally the planar dimer model) turns out to have remarkable connections with other parts of mathematics, from conformal field theory to integrable systems to representation theory.

Webs are representation-theoretic objects, defined by Greg Kuperberg to study invariants in tensor products of SL(3) representations. In these lectures I will discuss recent results on large-scale structures (webs) in random multiple-domino tilings, and their conformal invariance properties. 

The lectures are based on joint work with David Wilson, Daniel Douglas, Haolin Shi.

About the 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. 

About William Paul Thurston

William Paul Thurston (October 30, 1946 – August 21, 2012) was among the most original and influential mathematicians of the twentieth century. He transformed the mathematics of foliations, low-dimensional topology, hyperbolic manifolds, the theory of rational maps, and geometric group theory. His work led to a fundamental rethinking of the structure of 3-dimensional spaces.

Thurston received a bachelor's degree from New College in 1967 and a Ph.D. in Mathematics from UC Berkeley in 1972. He spent a year at the Institute for Advanced Study and a year at MIT before being appointed Professor of Mathematics at Princeton University in 1974. In 1991 he moved to UC Berkeley and in 1993 he was appointed Director of the Mathematical Sciences Research Institute. In 1996 he moved again, this time to UC Davis, where he was a Professor of Mathematics until 2003, when he moved to Cornell.  Bill was in the process of returning to UC Davis in 2012 when he tragically passed away.

Thurston’s work revealed the unexpectedly central role played by hyperbolic geometry in the study of low-dimensional manifolds.  His Geometrization Conjecture, which he solved in many cases, changed the fundamental viewpoint from which mathematicians approached the study of manifolds.

Thurston was awarded the Veblen Prize in Geometry in 1976, the Fields Medal at the 1983 International Congress of Mathematicians in Warsaw and the Leroy P. Steele Prize for seminal contribution to research in 2012. Thurston had numerous Ph.D. students, many of whom became leading mathematicians themselves.

"Mathematics is a process of staring hard enough with enough perseverence at the fog of muddle and confusion to eventually break through to improved clarity."

–Bill Thurston, "About me" on MathOverflow

2020 Lectures (Cancelled)

2019 Lectures

2018 Lectures

2017 Lectures