Consider the family of automorphic representations on some
unitary group with fixed (possibly non-tempered) cohomological
representation π0 at infinity and level dividing some finite upper
bound. We compute statistics of this family as the level...
Let G be a simply-connected complex semisimple algebraic group
and let C be a smooth projective curve of any genus. Then, the
moduli space of semistable G-bundles on C admits so called
determinant line bundles. E. Verlinde conjectured a
remarkable...
There is a celebrated connection between minimal (or constant
mean curvature) hypersurfaces and Ricci curvature in Riemannian
Geometry, often boiling down to the presence of a Ricci term in the
second variation formula for the area. The first goal...
A famous conjecture of Littlewood states that the Fourier
transform of every set of N integers has l^1 norm at least log(N),
up to a constant multiplicative factor. This was proved
independently by McGehee-Pigno-Smith and Konyagin in the 1980s.
This...
Humans have been thinking about polynomial equations over the
integers, or over the rational numbers, for many years. Despite
this, their secrets are tightly locked up and it is hard to know
what to expect, even in simple looking cases. In this talk...
A meandric system of size $n$ is the set of loops formed from
two arc diagrams (non-crossing perfect matchings) on
$\{1,\dots,2n\}$, one drawn above the real line and the other below
the real line. Equivalently, a meandric system is a coupled...
A subset of a group is said to be product free if it does not
contain the product of two elements in it. We consider how large
can a product free subset of the alternating group An be?
In the talk we will completely solve the problem by...
Approximate lattices in locally compact groups are approximate
subgroups that are discrete and have finite co-volume. They provide
natural examples of objects at the intersection of algebraic
groups, ergodic theory and additive combinatorics... with...
Work of Mark Shusterman and myself has proven an analogue of
Chowla's conjecture for polynomial rings over finite fields, which
controls k-points correlations of the Möbius function for k bounded
by a certain function of the finite field size...
