Abstract: Over the past two years Church, Ellenberg, Farb, and Nagpal developed a framework for studying sequences of representations of the symmetric groups, using a concept they call an FI--module. I will give an overview of this theory, and describe how it generalizes to sequences of representations of the Weyl groups in type B/C and D. I will outline some applications, including stability results for the cohomology of hyperplane complements, and of families of groups related to the braid groups.
(Note: The talk should be accessible to graduate students.)