This is a review article on the quantum toroidal algebras, focusing on their roles in various
solvable structures of 2d conformal field theory, supersymmetric gauge theory, and string …

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 …

We define and study a sheaf-theoretic cohomological Hall algebra for suitably geometric
Abelian categories $\mathcal {A} $ of homological dimension at most two, and a sheaf …

We determine the structure of the BPS algebra of $2 $-Calabi-Yau Abelian categories
whose stack of objects admits a good moduli space. We prove that this algebra is …

We introduce for each quiver Q and each algebraic oriented cohomology theory A, the
cohomological Hall algebra (CoHA) of Q, as the A‐homology of the moduli of …

Abstract We study the Borel–Moore homology of stacks of representations of preprojective
algebras Π Q, via the study of the DT theory of the undeformed 3-Calabi–Yau completion Π …

We prove that the K-theoretic Hall algebra of a preprojective algebra of affine type is
isomorphic to the positive half of a quantum toroidal quantum group. We also compare super …

For a smooth quasi-projective surface S over C we consider the Borel–Moore homology of
the stack of coherent sheaves on S with compact support and make this space into an …

We introduce a new perverse filtration on the Borel-Moore homology of the stack of
representations of a preprojective algebra $\Pi_Q $, for arbitrary $ Q $, by proving that the …

Given a quiver with potential $(Q, W) $, Kontsevich–Soibelman constructed a cohomological
Hall algebra (CoHA) on the critical cohomology of the stack of representations of $(Q, W) …