Catherine Wolfram - The dimer model in 3D

Описание: This talk is a part of the thematic trimester: Integrable systems of the Seed Seminar of Mathematics and Physics

Speaker: Catherine Wolfram (MIT)

Title: The dimer model in 3D

Abstract: A dimer tiling of ℤ^d is a collection of edges such that every vertex is covered exactly once. In 2000, Cohn, Kenyon, and Propp showed that 2D dimer tilings satisfy a large deviations principle. In joint work with Nishant Chandgotia and Scott Sheffield, we prove an analogous large deviations principle for dimers in 3D. A lot of the results for dimers in two dimensions use tools and exact formulas (e.g. the height function representation of a tiling or the Kasteleyn determinant formula) that are specific to dimension 2. I will explain how to formulate the large deviations principle in 3D, show simulations, and try to give some intuition for why three dimensions is different from two. Time permitting, I will explain some of the ways that we use a smaller set of tools (e.g. Hall’s matching theorem or a double dimer swapping operation) in our arguments.

Presented on Tuesday, April 23, 2024, at 3 p.m. (Paris time)

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