EVENT DETAILS AND ABSTRACT

Title: Twisted commutative algebras
Speaker: Steven Sam
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Abstract: Twisted commutative algebras are commutative rings with an action of the infinite general linear group and are connected with recent studies of "representation stability". The simplest nontrivial example of a twisted commutative algebra is the infinite polynomial ring C[x_1, x_2, ...] with the natural action of GL(infinity). Its module category is equivalent to the category of (complex) FI-modules, which was recently introduced by Church-Ellenberg-Farb to study cohomology of configuration spaces and many other examples. In this talk I will explain joint work with Andrew Snowden on the structural properties of this category and the connection to FI-modules. Time permitting, I will explain what we know about more complicated twisted commutative algebras and their connections with representation stability.