D-modules continues to be an active area of stimulating research in such mathematical
areas as algebra, analysis, differential equations, and representation theory. Key to D …

Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a
singular space into smooth manifolds, a great geometrical idea due to R. Thom and H …

We define a new type of Hall algebras associated eg with quivers with polynomial potentials.
The main difference with the conventional definition is that we use cohomology of the stack …

We define an action of the (double of) Cohomological Hall algebra of Kontsevich and
Soibelman on the cohomology of the moduli space of spiked instantons of Nekrasov. We …

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

Let F be a local field of characteristic zero and G be a connected reductive linear algebraic
group over F. According to the local Langlands conjecture, the set Π (G (F)) of isomorphism …

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 …

This paper is concerned with a non-compact GIT quotient of a vector space, in the presence
of an abelian group action and an equivariant regular function (potential) on the quotient …

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 …