## EVENT DETAILS AND ABSTRACT

**Geometry/Physics Seminar**
**Title:** Kasteleyn operators from mirror symmetry

**Speaker:** Harold Williams

**Speaker Info:** UC Davis

**Brief Description:** Research talk

**Special Note**:

**Abstract:**

Given a consistent bipartite graph $\Gamma$ in $T^2$ with a complex-valued edge weighting $\mathcal{E}$ we show the following two constructions are the same. The first is to form the Kasteleyn operator of $(\Gamma, \mathcal{E})$ and pass to its spectral transform, a coherent sheaf supported on a spectral curve in $(\mathcal{C}^\times)^2$. The second is to form the conjugate Lagrangian $L \subset T^* T^2$ of $\Gamma$, equip it with a brane structure prescribed by $\mathcal{E}$, and pass to its mirror coherent sheaf. This lives on a stacky toric compactification of $(\mathcal{C}^\times)^2$ determined by the Legendrian link which lifts the zig-zag paths of $\Gamma$ (and to which the noncompact Lagrangian $L$ is asymptotic). We work in the setting of the coherent-constructible correspondence, a sheaf-theoretic model of toric mirror symmetry. This is joint work with David Treumann and Eric Zaslow.

**Date:** Thursday, November 1, 2018

**Time:** 4:10pm

**Where:** Lunt 107

**Contact Person:** Bahar Acu

**Contact email:** baharacu@northwestern.edu

**Contact Phone:**

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