#### Kick-off event: Wednesday, November 6 afternoon at Institut Henri PoincarÃ©

Infos and registration: https://indico.math.cnrs.fr/e/NTQFTMR

# The dimer model in 3D

*by*

### Catherine 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. Hallâ€™s matching theorem or a double dimer swapping operation) in our arguments.

All talks Fall '24: New trends in QFT, modularity, resurgence