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Geometry, Symmetry and Physics Seminar

Non-archimedean mirrors of symplectic cluster manifolds in real dimension 4

Umut Varolgunes, Stanford

Location:  Webex - email organizers
Date & time: Thursday, 14 May 2020 at 2:00PM - 3:00PM

 I will start by explaining what I mean by a symplectic cluster manifold and how to represent them by certain combinatorial data called an eigenray diagram (4d only!). These manifolds admit a Lagrangian fibration over the real plane with only focus-focus singularities. They do not need to have convex boundary or exact symplectic form, but they are open and geometrically bounded. Eigenray diagrams are related to toric models and the relation will be briefly mentioned. Then, using relative symplectic cohomology and a locality statement that relies on monotonicity techniques, I will describe conjectural mirrors of symplectic cluster varieties as certain deformed (over the Novikov field) cluster varieties. I will also briefly explain the step to go from this to homological mirror symmetry, which is ongoing work. Our construction generalizes, from a purely symplectic perspective and in various directions, the works of Gross, Hacking, Keel, Kontsevich, and Siebert. This is joint work with Yoel Groman.

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