Seminar Event Detail


Combinatorics

Date:  Friday, February 09, 2018
Location:  4088 East Hall (4:10 PM to 5:00 PM)

Title:  Families of nested graphs with compatible symmetric-group actions

Abstract:   For fixed positive integers n and k, the Kneser graph has vertices labeled by k-element subsets of {1,2,…,n} and edges between disjoint sets. Keeping k fixed and allowing n to grow, one obtains a family of nested graphs, each of which is acted on by a symmetric group in a way which is compatible with all of the other actions. In this paper, we provide a framework for studying families of this kind using the FI-module theory of Church, Ellenberg, and Farb, and show that this theory has a variety of asymptotic consequences for such families of graphs. These consequences span a range of topics including enumeration, concerning counting occurrences of subgraphs, topology, concerning Hom-complexes and configuration spaces of the graphs, and algebra, concerning the changing behaviors in the graph spectra.

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Speaker:  Eric Ramos
Institution:  U. Michigan

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