I'll present joint work with Tsao-Hsien Chen on the geometry of
real and symmetric matrices. For classical groups, we use
hyperkahler geometry to lift the Kostant-Sekiguchi correspondence
to an equivariant homeomorphism. As an application, we show...
Polymers are macromolecules that cannot cross each other without
breaking their bonds. This leads to polymer chain entanglement
which determines bulk viscoelastic responses of the material.
Understanding the relation between entanglement and...
Triangulated categories play an important role in symplectic
topology. The aim of this talk is to explain how to combine
triangulated structures with persistence module theory in a
geometrically meaningful way. The guiding principle comes from
the...
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...
