Representations of Combinatorial Categories

Abstract: 

My plan is to give an example-oriented introduction to the subject of representations of combinatorial categories.  The main examples will be cohomology groups of configuration spaces of manifolds, homology groups of configuration spaces of graphs, and Kazhdan-Lusztig coefficients of graphs.  The goal will be to understand how Noetherianity results about the relevant categories can shed light on each of these examples.