Flavors of Amplitudes
Kick-off event on Wed 28.01.26 at Institut Henri Poincaré. Inscriptions: link indico
The seminars at IHES will take place on the following Wednesdays: 4.02, 18.02 and 18.03, see program
The dimer model in 3D
byCatherine Wolfram
Abstract:A dimer tiling of \( \mathbb{Z}^d \) 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.