Alexander F. Ritter

Deformations of Symplectic Cohomology and Exact Lagrangians in ALE Spaces

ALE spaces are the simply connected hyperkähler manifolds which at infinity look like

Novikov-symplectic cohomology and exact Lagrangian embeddings

{\mathbb{C}^{2}/G}

Circle actions, quantum cohomology, and the Fukaya category of Fano toric varieties

, for any finite subgroup

The wrapped Fukaya category of a negative line bundle

{G \subset SL_2(\mathbb{C})}

Invariance of symplectic cohomology and twisted cotangent bundles over surfaces.

. We prove that all exact Lagrangians inside ALE spaces must be spheres. The proof relies on showing the vanishing of a twisted version of symplectic cohomology.This application is a consequence of a general deformation technique. We construct the symplectic cohomology for non-exact symplectic manifolds, and we prove that if the non-exact symplectic form is sufficiently close to an exact one then the symplectic cohomology coincides with an appropriately twisted version of the symplectic cohomology for the exact form.

The McKay correspondence via Floer theory

We build the wrapped Fukaya category