The Generalized Ramanujan Conjecture (GRC) for GL(n) is a
central open problem in modern number theory. Its resolution is
known to yield several important applications. For instance, the
Ramanujan-Petersson conjecture for GL(2), proven by Deligne...
Given a representation of a reductive group,
Braverman-Finkelberg-Nakajima defined a Poisson variety called the
Coulomb branch, using a convolution algebra construction. This
variety comes with a natural deformation quantization, called a
Coulomb...
For a finite group G one has a process of modular reduction
which takes a KG-module, over a field K of characteristic zero, and
produces a kG-module, over a field k of positive characteristic.
Starting with a simple KG-module its modular reduction...
Reverse plane partitions - or RPPs for short - are order
reversing maps of minuscule posets in types ADE. We report on joint
work in progress with Elek, Kamnitzer, Libman, and Morton-Ferguson
in which we give a type independent proof that RPPs form...
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...
