The language edit distance is a significant generalization of
two basic problems in computer science: parsing and string edit
distance computation. Given any context free grammar, it computes
the minimum number of insertions, deletions and...
I will give examples and motivations, about the local systems/Higgs
bundles correspondence, the case of variations of Hodge structures
and the case of irregular singularities. I hope this will help to
enjoy the forthcoming lectures of T. Mochizuki...
Let $D$ be a central division algebra of degree $n$ over a field
$K$. One defines the genus gen$(D)$ of $D$ as the set of classes
$[D']$ in the Brauer group Br$(K)$ where $D'$ is a central division
$K$-algebra of degree $n$ having the same...
I will consider the energy-critical wave maps equation with values
in the sphere in the equivariant case, that is for symmetric
initial data. It is known that if the initial data has small
energy, then the corresponding solution scatters. Moreover...
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...
