Our goal is to explain how certain basic representation
theoretic ideas and constructions encapsulated in the form of
Macdonald processes lead to nontrivial asymptotic results in
various `integrable'; probabilistic problems. Examples include
dimer...
In this lecture, I will talk about moment based SDP hierarchies
(which are duals of SOS relaxations for polynomial optimization) in
the context of graph partitioning. The focus will be on a certain
way of rounding such hierarchies, whose quality is...
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...
For a permutation p, let Sn(p) be the number of permutations on
n letters avoiding p. Stanley and Wilf conjectured that, for each
permutation p, Sn(p)1/n tends to a finite limit L(p). Marcus and
Tardos proved the Stanley-Wilf conjecture by a...
