Anders Buch, Rutgers University

Jeff Kahn, Rutgers University

Abstract

Title: Trees and Degrees

Speaker: Jeff Kahn, Rutgers

I'll mention a few problems on tree counts in graphs and, as time permits, try to say a little about what these might have to do with one or two topics (random methods, entropy) that I like.

Title: Schur Polynomials and the Littlewood-Richardson Rule

Speaker: Anders Buch, Rutgers

The ring of symmetric polynomials in a list of variables has a basis consisting of Schur polynomials that is related to many areas in mathematics, including representation theory of GL(n), geometry of Grassmannians, eigenvalues of Hermitian matrices, statistics, and complexity theory. The coefficients obtained when a product of two Schur polynomials is expanded in the basis of Schur polynomials are called Littlewood-Richardson coefficients. The classical Littlewood-Richardson rule expresses these coefficients as the number of ways of filling a diagram of boxes with integers satisfying certain conditions. I will speak about these basic notions, which are important in many parts of mathematics and have inspired many developments within combinatorics.