We construct knot invariants categorifying the quantum knot variants for all representations
of quantum groups. We show that these invariants coincide with previous invariants defined …

We study quantizations of transverse slices to Schubert varieties in the affine Grassmannian.
The quantization is constructed using quantum groups called shifted Yangians—these are …

The dazzling success of algebraic geometry... has so much reorientated the field that one
particular protagonist has suggested, no doubt with much justification, that enveloping …

We re-examine some topics in representation theory of Lie algebras and Springer theory in
a more general context, viewing the universal enveloping algebra as an example of the …

We prove a conjecture of Rouquier relating the decomposition numbers in category for a
cyclotomic rational Cherednik algebra, including the connection of decomposition numbers …

Truncated shifted Yangians are a family of algebras which are natural quantizations of slices
in the affine Grassmannian. We study the highest weight representations of these algebras …

We study the representation theory of the invariant subalgebra of the Weyl algebra under a
torus action, which we call a “hypertoric enveloping algebra”. We define an analogue of …

In this paper, we give a method for relating the generalized category OO defined by the
author and collaborators to explicit finitely presented algebras, and apply this to quiver …

We construct knot invariants categorifying the quantum knot variants for all representations
of quantum groups. We show that these invariants coincide with previous invariants defined …

In this paper, we describe a categorical action of any symmetric Kac–Moody algebra on a
category of quantized coherent sheaves on Nakajima quiver varieties. By “quantized …