We give a diagrammatic presentation in terms of generators and relations of the
representation category of U_q (sl _n) U q (sl n). More precisely, we produce all the relations …

We give an elementary construction of colored sl n link homology. The invariant takes values
in a 2-category where 2-morphisms are given by foams, singular cobordisms between sl n …

An idempotented form U (sln) of the quantum enveloping algebra of sln was introduced by
Beilinson-Lusztig-MacPherson [1], who also related it to the geometry of partial flag varieties …

We show that Khovanov homology (and its sl 3 variant) can be understood in the context of
higher representation theory. Specifically, we show that the combinatorially defined foam …

Given a finite subgroup Γ⊂ SL 2 (C) we define an additive 2-category H Γ whose
Grothendieck group is isomorphic to an integral form h Γ of the Heisenberg algebra. We …

We categorify all the Reshetikhin–Turaev tangle invariants of type A. Our main tool is a
categorification of the generalized Jones–Wenzl projectors (aka clasps) as infinite twists …

Given a strong 2-representation of a Kac–Moody Lie algebra (in the sense of Rouquier), we
show how to extend it to a 2-representation of categorified quantum groups (in the sense of …

We prove a conjectured decomposition of deformed sl N link homology, as well as an
extension to the case of colored links, generalizing results of Lee, Gornik, and Wu. To this …

This paper studies the derived category of the Quot scheme of rank $ d $ locally free
quotients of a sheaf $\mathscr {G} $ of homological dimension $\le 1$ over a scheme $ X …

We introduce an $\mathfrak {sl} _n $ homology theory for knots and links in the thickened
annulus. To do so, we first give a fresh perspective on sutured annular Khovanov homology …