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Terrence George: Generalized shufflings in the dimer model

Time: Tue 2021-10-26 15.15

Location: Zoom, meeting ID: 698 3346 0369

Lecturer: Terrence George (University of Michigan)

Abstract

Domino-shuffling is a technique introduced by Elkies, Kuperberg, Larsen and Propp to enumerate and generate domino tilings of the Aztec diamond graph, and was used to give the first proof of the arctic circle theorem. Domino tilings are dual to the dimer model on the square lattice. There are generalizations of domino-shuffling for any biperiodic dimer model, and they form a group called the cluster modular group. This group was studied by Fock and Marshakov, who gave an explicit conjecture for its isomorphism type. We will discuss these generalized shufflings and how to compute the cluster modular group for any biperiodic dimer model.