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...
In 1979, O. Heilmann and E.H. Lieb introduced an interacting dimer
model with the goal of proving the emergence of a nematic liquid
crystal phase in it. In such a phase, dimers spontaneously align,
but there is no long range translational order...
The generalised Kato classes of Darmon-Rotger arise as $p$-adic
limits of diagonal cycles on triple products of modular curves, and
in some cases, they are predicted to have a bearing on the
arithmetic of elliptic curves over $Q$ of rank two. In...
