The matching polynomial of a discrete graph encodes information that holds interest to mathematicians and non-mathematicians (i.e. physicists and chemists). In this talk we will discuss asymptotic "high-temperature" behavior of this invariant on k-regular graphs, following recent work of Csikvari (2014). Our main tool is to relate the matching polynomial of a graph to that of its bipartite double cover.

[If you're not yet convinced this belongs in a combinatorics seminar: the Catalan numbers make an unexpected appearance!] Speaker(s): Harry Richman (University of Michigan)