This is the first of a series of papers about quantization in the context of derived algebraic
geometry. In this first part, we introduce the notion of n-shifted symplectic structures (n …

Factorization algebras are local-to-global objects that play a role in classical and quantum
field theory that is similar to the role of sheaves in geometry: they conveniently organize …

The purpose of this work is to prove the existence of an algebraic moduli classifying objects
in a given triangulated category. To any dg-category T (over some base ring k), we define a …

We study the interaction between geometric operations on stacks and algebraic operations
on their categories of sheaves. We work in the general setting of derived algebraic …

We develop a framework for derived deformation theory, valid in all characteristics. This
gives a model category reconciling local and global approaches to derived moduli theory. In …

Many interesting spaces—including all positroid strata and wild character varieties—are
moduli of constructible sheaves on a surface with microsupport in a Legendrian link. We …

A `Darboux theorem' for shifted symplectic structures on derived Artin stacks, with applications
Page 1 msp Geometry & Topology 19 (2015) 1287–1359 A ‘Darboux theorem’ for shifted …

We study the unwrapped Fukaya category of Lagrangian branes ending on a Legendrian
knot. Our knots live at contact infinity in the cotangent bundle of a surface, the Fukaya …

Abstract Let (X, ω X∗) be a separated,− 2–shifted symplectic derived ℂ–scheme, in the
sense of Pantev, Toën, Vezzosi and Vaquié (2013), of complex virtual dimension vdim ℂ X …

Enumerative invariants in Algebraic Geometry'count'$\tau $-(semi) stable objects $ E $ with
fixed topological invariants $[E]= a $ in some geometric problem, using a virtual class $[{\cal …