The notion of exactly (or approximately) representing certain
combinatorial properties of a graph $G$ on a simpler graph is
ubiquitous in combinatorial optimization. In this talk, I will
introduce the notion of vertex sparsification. Here we are...
I will describe the notions of strong and weak epsilon nets in
range spaces, and explain briefly some of their many applications
in Discrete Geometry and Combinatorics, focusing on several recent
results in the investigation of the extremal...
A long-standing line of work in economic theory has studied
models by which a group of people in a social network, each holding
a numerical opinion, can arrive at a shared opinion through
repeated averaging with their neighbors in the network...
We consider asymptotics of the correlation functions of
characteristic polynomials of the hermitian Wigner matrices
$H_n=n^{-1/2}W_n$ and the hermitian sample covariance matrices
$X_n=n^{-1}A_{m,n}^*A_{m,n}$. We use the integration over
the...
