Tri Lai

Title: Enumeration of Tilings and Related Problems

Abstract: The field of enumeration of tilings dates back to the early 1900s when Percy MacMahon proved his classical theorem on plane partitions. The enumeration of tilings has since taken on a life of its own as a subfield of combinatorics with connections and applications to diverse areas of mathematics, including representation theory, linear algebra, group theory, mathematical physics, graph theory, probability, and cluster algebra, just to name a few. In this talk, we focus on an interesting connection between tilings, linear algebra, and a mathematical model of electrical networks. In particular, we will go over the proof of a conjecture of Kenyon and Wilson on `tiling-representation’ of semi-contiguous minors.