I describe recent results on spiked covariance matrices, which
model multivariate data containing nontrivial correlations. In
principal components analysis, one extracts the leading
contribution to the covariance by analysing the top eigenvalues
and...
I will present some recent applications of symplectic geometry to
the restricted three body problem. More specifically, I will
discuss how Gromov's original study of pseudoholomorphic curves in
the complex projective plane has led to the...
The study of random Cayley graphs of finite groups is related to
the investigation of Expanders and to problems in Combinatorial
Number Theory and in Information Theory. I will discuss this topic,
describing the motivation and focusing on the...
A widely studied model from statistical physics consists of many
(one-dimensional) Brownian motions interacting through a pair
potential. The large scale behavior of this model has has been
investigated by Varadhan, Yau, and others in the 90's. As a...
This is intended to be a survey talk, accessible to a general
mathematical audience. The cdh topology was created by Voevodsky to
extend motivic cohomology from smooth varieties to singular
varieties, assuming resolution of singularities (for...
We will review some interactions between random matrix theory
and distributions of zeroes of L-functions in families (the
Katz-Sarnak philosophy) before presenting some recent results
(joint with Dorian Goldfeld) in the higher rank setting. We
will...
We discuss the classical and non-commutative geometry of wire
systems which are the complement of triply periodic surfaces. We
consider a C∗-geometry that models their electronic properties. In
the presence of an ambient magnetic field, the relevant...
In this seminar, we will discuss the recent work on the
eigenvalue and eigenvector distributions of random matrices. We
will discuss a dynamical approach to these problems and related
open questions. We will discuss both Wigner type matrix
ensembles...
