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 …

This expository article explains how planar diagrammatics naturally arise in the study of
categorified quantum groups with a focus on the categorification of quantum sl2. We derive …

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 …

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 …

The theory of $\Theta $-stratifications generalizes a classical stratification of the moduli of
vector bundles on a smooth curve, the Harder-Narasimhan-Shatz stratification, to any moduli …

We show that for many moduli spaces of torsion sheaves on K3 surfaces, the functor
induced by the universal sheaf is a-functor, hence can be used to construct an …

We compute the number of finite dimensional irreducible modules for the algebras
quantizing Nakajima quiver varieties. We get a lower bound for all quivers and vectors of …

We introduce the idea of a geometric categorical Lie algebra action on derived categories of
coherent sheaves. The main result is that such an action induces an action of the braid …