Speaker: Steven Sam, University of California, Berkeley, and the University of Wisconsin-Madison

Title: Schur-Weyl duality and generalizations

Abstract: I'll begin my talks describing the classical relationship between representations of the symmetric group, the general linear group, and symmetric functions. When the general linear group is replaced by a classical group such as the orthogonal group or symplectic group, the symmetric group is replaced by the Brauer algebra, and there still remains a connection to symmetric functions, but complications arise. A systematic investigation of these complications leads one to the study of "twisted commutative algebras" and representations of categories which generalize diagram algebras like the Brauer algebra. These are algebraic structures of a combinatorial nature and connect with some topics in algebraic geometry and topology which I'll discuss as time permits. My goal with these lectures is to survey some joint work with Andrew Snowden on these topics; the intent is to keep the lectures at an accessible level.