Colloquium abstracts

Rohit Nagpal
University of Chicago, USA
July 6, 2017

Representation stability and FI-modules:  We often encounter sequences of representations of a family of groups. For example, the cohomology of ordered configurations of $n$​ distinct points on a manifold is a representation of the symmetric group $S_n$​ Similarly, the homology of the congruence subgroup of level $m$​ inside $GL_n(Z)$​ is a representation of $GL_n(Z/mZ)$​. As $n$​ grows to infinity the two examples above become, in a sense, stable as representations. Stable representations can be thought of as finitely generated objects in a suitable functor category. This point of view is due to Church-Ellenberg-Farb who introduced and studied such a category called FI-modules. We provide an introduction to FI-modules and explain what it entails about the examples above.