We will describe an implementation of the Wiener theorem in $L^1$
type convolution algebras in the setting of spectral theory. In
joint work with Marius Beceanu we obtained a structure theorem for
the wave operators by this method.
In 1880, Markoff studied a cubic Diophantine equation in three
variables now known as the Markoff equation, and observed that its
integral solutions satisfy a form of nonlinear descent.
Generalizing this, we consider families of log Calabi-Yau...
A cap set in $(F_q)^n$ is a set not containing a three term
arithmetic progression. Last year, in a surprising breakthrough,
Croot-Lev-Pach and a follow up paper of Ellenberg-Gijswijt showed
that such sets have to be of size at most $c^n$ with $c q...
We will discuss how to study the symplectic geometry of
$2n$-dimensional Weinstein manifolds via the topology of a core
$n$-dimensional complex called the skeleton. We show that the
Weinstein structure can be homotoped to admit a skeleton with a...
In this talk, I will discuss the behavior of hard-core lattice
particle systems at high fugacities. I will first present a
collection of models in which the high fugacity phase can be
understood by expanding in powers of the inverse of the fugacity...
A weight-$t$ halfspace is a Boolean function
$f(x)=\mathrm{sign}(w_1 x_1 + \cdots + w_n x_n - \theta)$ where
each $w_i$ is an integer in $\{-t,\dots,t\}.$ We give an explicit
pseudorandom generator that $\delta$-fools any intersection of $k$
weight...
Let $E$ be a CM elliptic curves over rationals and $p$ an odd prime
ordinary for $E$. If the $\mathbb Z_p$ corank of $p^\infty$ Selmer
group for $E$ equals one, then we show that the analytic rank of
$E$ also equals one. This is joint work with...
We present a new approach to the existence of time quasi-periodic
solutions to nonlinear PDE's. It is based on the method of Anderson
localization, harmonic analysis and algebraic analysis. This can be
viewed as an infinite dimensional analogue of a...
