Since its inception around 1980, the theory of perverse sheaves has been a vital tool of
fundamental importance in geometric representation theory. This book, which aims to make …

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 …

This paper concerns the cohomological aspects of Donaldson–Thomas theory for Jacobi
algebras and the associated cohomological Hall algebra, introduced by Kontsevich and …

Let $ U $ be a smooth $\mathbb C $-scheme, $ f: U\to\mathbb A^ 1$ a regular function, and
$ X= $ Crit $(f) $ the critical locus, as a $\mathbb C $-subscheme of $ U $. Then one can …

In recent years, intersection homology and perverse sheaves have become indispensable
tools for studying the topology of singular spaces. This book provides a gentle introduction to …

Pursuing the similarity between the Kontsevich–Soibelman construction of the
cohomological Hall algebra (CoHA) of BPS states and Lusztig's construction of canonical …

For oriented-shifted cotangent stack over a quasi-smooth derived Artin stack is isomorphic to
the Borel–Moore homology of the base stack up to a certain shift of degree. This is a global …

Let X be the canonical bundle of a smooth algebraic surface S. We construct the (sheaf-
level) 3d or critical cohomological Hall algebra of X. This refines the 2d cohomological Hall …

We present a detailed introduction of the theory of constructible sheaf complexes in the
complex algebraic and analytic setting. All concepts are illustrated by many interesting …

Let $\mathfrak {g} $ be a simple Lie algebra over $\mathbb {C} $. The KZ connection is a
connection on the constant bundle associated to a set of $ n $ finite dimensional irreducible …