|Date: Tuesday, September 29, 2020
Location: Virtual (5:00 PM to 6:00 PM)
Title: q-Series and applications to counting matrices
Abstract: This talk is suitable both as a learning seminar and as a research talk. The first part is a practical and hands-on introduction of "q-series", an assortment of power series arising from the enumeration of linear-algebraic objects and partitions of integers. I will present the proofs of a few combinatorial identities to introduce some standard tools to work with q-series. The second part of the talk is about my recent result of enumerating pairs of n x n matrices (A, B) with AB=BA=0 over finite fields. A proof using the standard toolkit will be given. I will then explain how this question is related to the algebraic geometry of nodal curves.
Speaker: Yifeng Huang