- Series
- Algebra Seminar
- Time
- Monday, August 25, 2025 - 1:00pm for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Alex McDonough – University of Oregon – https://sites.google.com/view/alexmcdonough/home
- Organizer
- Donggyu Kim
Please Note: There will be a pre-seminar 10:55-11:15 in Skiles 005.
Traditionally, chip-firing is a discrete dynamical system where poker chips move around the vertices of a graph. One fascinating result is that number of configurations of a fixed number of chips, modulo a firing equivalence relation, is the number of spanning trees of the graph. This relationship gives the set of spanning trees group-like properties.
In this talk, I will discuss how chip-firing ideas can be generalized from graphs to regular matroids, where bases play the role of spanning trees. This will lead to an overview of joint work with Ding, Tóthmérész, and Yuen on the consistency of the Backman-Baker-Yuen Sandpile Torsor.
============(Below is the information on the pre-talk.)============
Title (pre-talk): Transforming Spanning Trees Using Mathematicians and Coffee Cups
Abstract (pre-talk): There is a fascinating structure to the set of spanning trees of a plane graph, which allows this set to behave much like a group. Perhaps most incredibly, there is a sense in which this structure is canonical.
In this talk, I will show you how spanning trees can be transformed after introducing mathematicians and coffee cups on some of the vertices. This is a variant of the rotor-routing process which takes advantage of a special property of plane graphs.