The theta correspondence of Roger Howe gives a way to connect
representations of different classical groups. We aim to geometrize
the theta correspondence for groups over finite fields in the
spirit of Lusztig's character sheaves. Given a reductive...
Indistinguishability obfuscation, introduced by [Barak et. al.
Crypto’2001], aims to compile programs into unintelligible ones
while preserving functionality. It is a fascinating and powerful
object that has been shown to enable a host of new...
Let X be a compact symplectic manifold, and D a normal crossings
symplectic divisor in X. We give a criterion under which the
quantum cohomology of X is the cohomology of a natural deformation
of the symplectic cochain complex of X \ D. The...
Let \o be an order in a totally real field, say F. Let K be an
odd-degree totally real field. Let S be a finite set of places of
K. We study S-integral K-points on integral models H_\o of Hilbert
modular varieties because not only do said varieties...
This talk will be an exposition of a recent paper of
Bezrukavnikov-Gaitsgory-Mirkovic-Riche-Rider giving an
Iwahori-Whittaker model for the Satake category. The main point is
that their argument works for modular coefficients. I will give
some...
A sofic approximation to a countable discrete group is a
sequence of finite models for the group that generalizes the
concept of a Folner sequence witnessing amenability of a group and
the concept of a sequence of quotients witnessing residual...
The modular representation theory of a finite group naturally
breaks into different pieces called blocks, and the defect of a
block is a sort of measure of its complexity. I will recall some
basic aspects of this theory, and then give the complete...
Motivated by some work of Thurston on defining a Teichmuller
theory based on best Lipschitz maps between surfaces, we study
infinity-harmonic maps from a manifold to a circle. The best
Lipschitz constant is taken on on a geodesic lamination...
There are striking analogies between topology and arithmetic
algebraic geometry, which studies the behavior of solutions to
polynomial equations in arithmetic rings. One expression of these
analogies is through the theory of etale cohomology, which...
Suppose we have a cancellative binary associative operation * on
a finite set X. We say that it is delta-associative if the
proportion of triples x, y, z such that x*(y*z) = (x*y)*z is at
least delta.
