Combinatorics Seminars-Counting partitions, Dynkin diagrams, quantum dilogarithms, and generalizations

Speaker: Justin Allman, USNA
Date and time: Thursday, October 11, 4–5 pm
Place: Phillips 110
Title: Counting partitions, Dynkin diagrams, quantum dilogarithms, and generalizations
Abstract: The Durfee's square identity is an effective way to iteratively count partitions going back to at least Cauchy. In this talk we show how this identity is related to representations of a certain quiver, namely an orientation of the A_2 Dynkin diagram. Furthermore, we show that identities among quantum dilogarithm series, with a rich history in their own right, can encode infinitely many of these Durfee's-square-type identities simultaneously. Finally, we discuss how these identities generalize to entire families of quivers.