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

Abstract: I will start by explaining what I mean by a symplectic cluster manifold focusing on how to represent them by certain combinatorial data called an eigenray diagram (4d only!). These symplectic 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 manifolds as certain deformed (over the Novikov field) cluster varieties. This is joint work with Yoel Groman.

algebraic geometrysymplectic geometry

Audience: researchers in the topic

M-seminar