Writing Down Polynomials via Representation Theory

Lecture 1: Writing Down Polynomials via Representation Theory I
Lecture 2: Writing Down Polynomials via Representation Theory II
 

This series of talks was part of the Algebraic Geometry Boot Camp. Videos for each talk are available through the links above.

Speaker: Christian Ikenmeyer, Texas A&M University

Starting with Schur-Weyl duality, we explain how polynomials can be written down as symmetrizations of highest weight vectors in a tensor power of C^n. Studying these polynomials leads to interesting questions in combinatorics, for example a famous conjecture about Latin Squares by Alon and Tarsi. Our goal is to explain the results of the three recent papers by Kadish and Landsberg, Bürgisser and Ikenmeyer, and Kumar, which all can be treated nicely in this framework.