** 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.