We revisit the definition of the Heisenberg category of central charge k∈ Z. For central
charge− 1, this category was introduced originally by Khovanov, but with some additional …

We introduce a diagrammatic monoidal category ℋ eisk (z, t) which we call the quantum
Heisenberg category; here, k∈ ℤ is “central charge” and z and t are invertible parameters …

We associate a monoidal category H λ to each dominant integral weight λ of sl ˆ p or sl∞.
These categories, defined in terms of planar diagrams, act naturally on categories of …

We associate a diagrammatic monoidal category Heis k (A; z, t), which we call the quantum
Frobenius Heisenberg category, to a symmetric Frobenius superalgebra A, a central charge …

We study the structure and representation theory of affine wreath product algebras and their
cyclotomic quotients. These algebras, which appear naturally in Heisenberg categorification …

These are lecture notes for a mini-course given at the conference Interactions of Quantum
Affine Algebras with Cluster Algebras, Current Algebras, and Categorification in June 2018 …

We provide an explicit formula for the following enumerative problem: how many
(absolutely) indecomposable vector bundles of a given rank r and degree d are there on a …

We compare the (horizontal) trace of the affine Hecke category with the elliptic Hall algebra,
thus obtaining an “affine” version of the construction of Gorsky et al.(Int. Math. Res. Not …

We categorify the commutation of Nakajima's Heisenberg operators action on the derived
category of Hilbert schemes. Our main technical tool is a detailed geometric study of certain …

We show that the central charge k reduction of the universal central extension of the elliptic
Hall algebra is isomorphic to the trace, or zeroth Hochschild homology, of the quantum …