I will review certain stabilization phenomena in the
characteristic zero representation theory of general linear and
symmetric groups as the rank tends to infinity. Then I will give a
survey of some results and conjectures about analogs of these
in...
Let G be a semi-simple algebraic group over an algebraically
closed field k of positive characteristic and let B be a Borel
subgroup. The cohomology of line bundles on the flag variety G/B
induced by characters of B are important objects in the...
Algebraic topologists talk about an elevator from characteristic
zero to characteristic p, with infinitely many floors in between
called chromatic levels. I think you could "do representation
theory" at any of these levels. I once tried to explore...
In this talk I will present a joint work with Arie Levit and
Yair Minsky on flexible stability of surface groups. The proof will
be geometric in nature and will rely on an analysis of branched
covers of hyperbolic surfaces. Along the way we will see...
We construct an explicit isomorphism between certain truncations
of quiver Hecke algebras and Elias-Williamson's diagrammatic
endomorphism algebras of Bott-Samelson bimodules. As a corollary,
we deduce that the decomposition numbers of these...
The Picard group of the stable module category of a finite group
plays a role in many parts of modular representation theory. It was
calculated when the group is an abelian p-group, by pioneering work
of Dade in the 1970's, and a classification for...
We explain an equivalence of categories between a module
category of quiver Hecke algebras associated with the Kronecker
quiver and a category of equivariant perverse coherent sheaves on
the nilpotent cone of type A. This provides a link between
two...
The geometric Satake equivalence establishes a link between two
categories: the category of spherical perverse sheaves on the
affine Grassmannian and the category of representations of the
Langlands dual group. It has found many important...
