Alex McDonough, Brown University

via Zoom
Note: This talk begins with a preseminar (aimed at graduate students) at 3:30–4:00. The main talk starts at 4:10.
Join Zoom Meeting: https://washington.zoom.us/j/
Meeting ID: 915 4733 5974
Traditionally, the sandpile group is defined on a graph and the MatrixTree Theorem says that this group's size is equal to the number of spanning trees. An extension of the MatrixTree Theorem gives a relationship between the sandpile group and bases of an orientable arithmetic matroid. I provide a family of combinatorially meaningful maps between these two sets. This generalizes a bijection given by Backman, Baker, and Yuen and extends work by Duval, Klivans, and Martin. I will not assume any background beyond undergraduate linear algebra.