**Title:** Gluing Fukaya categories of surfaces and singularity categories

**Speaker:** James Pascaleff

**Speaker Info:** University of Illinois at Urbana-Champaign

**Brief Description:**

**Special Note**:

**Abstract:**

Abstract: I will construct a sheaf of 2-periodic DG categories over decorated trivalent graphs. The sections of this sheaf over a given graph is a category that depends only on the number of loops g and the number of ends n, and in the case where n = 0, it also depends on a single continuous parameter. I will then show how this sheaf recoversA: The Fukaya category of a Riemann surface of genus g with n punctures with a particular total area,

B: The derived category of singularities of certain normal crossings surfaces, with a particular 2-periodic structure.

These results may be interpreted as mirror symmetry statements for Riemann surfaces.

(This is joint work with Nicolo Sibilla. I will try to avoid too much overlap with the talk that Nicolo gave recently.)

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