Dimer models and Hochschild cohomology

Michael Wong (University College London)

Wednesday 22nd May 16:00-17:00 Maths 311B

Abstract

A dimer model is a type of quiver embedded in a Riemann surface. It gives rise to an associative, generally noncommutative algebra called the Jacobi algebra. In the version of mirror symmetry proved by R. Bocklandt, the wrapped Fukaya category of a punctured surface is equivalent to the category of matrix factorizations of the Jacobi algebra of a dimer, equipped with its canonical potential. For the purposes of deformation theory, we explicitly describe the Hochschild cohomologies of the Jacobi algebra and the associated matrix factorization category in terms of dimer combinatorics.

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