Richard W. Kenyon, Erastus L. DeForest Professor of Mathematics at Yale University
Richard Kenyon received his PhD 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.
His central mathematical contributions are in statistical mechanics and geometric probability. He established the first rigorous results on the dimer model, opening the door to recent spectacular advances in the Schramm–Loewner evolution theory. In most recent work, he introduced new homotopic invariants of random structures on graphs, establishing an unforeseen connection between probability and representation theory.
Kenyon will give a series of three lectures on "Dimers and webs" from May 12-14, 2026.
Abstract: An n-web is an n-valent bipartite ribbon graph. (Planar) webs arise in representation theory: they are combinatorial devices used to understand invariants in tensor products of irreducible representations. Webs on surfaces can likewise be used to parameterize the character- or representation-variety of the surface.
Intriguingly, webs on surfaces also arise in the n-dimer model of statistical mechanics. In these lectures we discuss webs and their connection with the probability and statistical mechanics of the dimer model, giving a vast generalization of the classical Kasteleyn theorem which counts dimer covers (perfect matchings) of planar graphs.
These lectures are based on joint work with Dan Douglas, Nicholas Ovenhouse, Haolin Shi, Haihan Wu.
Lecture I: Webs, multiwebs, traces. The main theorem statement.
Tuesday, May 12, at 4pm in PACCAR Hall, PCAR 192.
(This is a joint talk with the Department of Applied Mathematics.)
Lecture II: SL_3 case: reduced webs, scaling limits. Connection to the 4-color theorem.
Wednesday, May 13, at 4pm in PACCAR Hall, PCAR 192.
Lecture III: Positive connections and generalizations.
Thursday, May 14, at 4pm in PACCAR Hall, PCAR 192.