Link spectral invariants and their homogenizations have been
defined by Cristofaro-Gardiner et.al. In joint work with Ibrahim
Trifa, we define a linear combination of such quasimorphism and
show that it vanishes on the stabilizer of the equator in...
A Hodge structure is a certain linear algebraic datum.
Importantly, the cohomology groups of any smooth projective
algebraic variety come equipped with Hodge structures which encode
the integrals of algebraic differential forms over
topological...
The theory of rigidity for lattices in higher rank semisimple
Lie groups is a powerful and exciting subject, combining methods
from algebra, number theory, geometry and dynamics. One of the most
celebrated results is Margulis' normal subgroup...
Around 1992, Aldous made the following bold conjecture. Let A be
any set of transpositions in the symmetric group Sym(N). Then
the spectral gap of the Cayley graph Cay(Sym(N),A)
is identical to that of a relatively tiny N-vertex graph
defined by A...
I'll give a brief introduction to o-minimality and how it can be
used to prove asymptotic estimates for the number of rational
points in definable sets. I'll then show how problems from various
areas of mathematics can be reformulated as questions...
In this talk, I will describe our construction of the first
explicit lossless vertex expanders. These are graphs where every
small subset of vertices has about as many neighbors as their
sparsity allows. Previously, the strongest known explicit...
The chord conjecture, due initially to Arnol'd in the case of
the standard contact three-sphere, asserts the existence of a Reeb
chord with boundary on every closed Legendrian submanifold of a
closed contact manifold for every contact form. This...
In characteristic zero, Castelnuovo proved that every
unirational surface is rational. In positive characteristic, this
fails dramatically: there exist many non-rational, often even
general-type, surfaces that are nevertheless unirational. In
1977...
I will describe recent work in progress on
logarithmic--exponential preparation theorems in analytically
generated sharply o-minimal structures. Our results imply the sharp
o-minimality of ℝexp
as well as a uniform version of Wilkie’s conjecture on...
