Peter Csikvari (ELTE): Schrijver's theorem on the number of perfect matchings and its variants

In this talk we will sketch a new proof of Schrijver's theorem. This theorem asserts that a $d$-regular bipartite graph on $2n$ vertices has at least $C_d^n$ perfect matchings, where $C_d=(d-1)^(d-1)/d^(d-2)$. (I will explain where the constant comes from.) The new proof uses ideas from graph limit theory, and relies on the work of Heilmann and Lieb concerning the matching polynomial. Then we will survey several further applications of the method. Every concept will be explained.