In this talk I will present the construction of combinatorial bases of standard modules with rectangular highest weights for affine Lie algebras, which relies on the construction of quasi--particle bases of the Feigin--Stoyanovsky principal subspaces. This talk is based on a joint project with S. Kozic and M. Primc.

In this talk, I will introduce the concept of a concrete L^p-correspondence over a pair of L^p-operator algebras. Definitions will be motivated by the C* results covered in my previous talk. Several examples of L^p-correspondences will be given and I will also show how, in some cases, we can get an L^p version of the Cuntz-Pimsner algebras. Time permitting, I will focus on L^p-modules, a particular type of L^p-correspondence that generalizes the notion of a Hilbert module, by presenting the current known theory and also discussing some open problems.

A random polynomial is a polynomial whose coefficients are random variables. A major task in the theory of random polynomials is to examine how the real roots are distributed and correlated in situations where the degree of the polynomial is large. In this talk, we examine two classes of random polynomials that have captured the attention of researchers in the fields of probability theory and mathematical physics: elliptic polynomials and generalized Kac polynomials.

Correlations between the real roots of random polynomials