The goal of these notes is to give a short introduction to Fukaya categories and some of their
applications. The first half of the text is devoted to a brief review of Lagrangian Floer (co) …

We consider mirror symmetry for (essentially arbitrary) hypersurfaces in (possibly
noncompact) toric varieties from the perspective of the Strominger-Yau-Zaslow (SYZ) …

In this paper we prove the smoothness of the moduli space of Landau–Ginzburg models. We
formulate and prove a Bogomolov–Tian–Todorov theorem for the deformations of Landau …

Inspired by the geometry of wrapped Fukaya categories, we introduce the notion of wrapped
microlocal sheaves. We show that traditional microlocal sheaves are equivalent to …

We associate a ring R to a log Calabi-Yau pair (X, D) or a degeneration of Calabi-Yau
manifolds X-> B. The vector space underlying R is determined by the tropicalization of (X, D) …

I provide two solutions to the problem of categorifying quantum link invariants, which work
uniformly for all gauge groups and originate in geometry and string theory. The first is based …

Twisted supergravity is supergravity in a background where the bosonic ghost field takes a
non-zero value. This is the supergravity counterpart of the familiar concept of twisting …

We build the wrapped Fukaya category W (E) W (E) for any monotone symplectic manifold E,
convex at infinity. We define the open-closed and closed-open string maps, OC: HH _*(W …

We prove a homological mirror symmetry result for maximally degenerating families of
hypersurfaces in (ℂ∗) n (B–model) and their mirror toric Landau–Ginzburg A–models. The …

Abstract We construct a Hamiltonian Floer theory-based invariant called relative symplectic
cohomology, which assigns a module over the Novikov ring to compact subsets of closed …