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### What is the sandpile torsor

**Algebra & Discrete Mathematics**

Speaker: | Alex McDonough, UC Davis |

Related Webpage: | https://sites.google.com/view/alexmcdonough/home |

Location: | 2112 MSB |

Start time: | Tue, May 14 2024, 11:00AM |

Let S be the set ofspanning treesof a given graph. Mathematicians have long been interested in calculating thecardinalityof S. However, there is more to explore about S than just its cardinality, and I am particularly interested in thestructureof this set. This talk will focus on a concrete construction based on therotor-routing algorithmwhich gives S a group-like structure. More precisely, we can understand S as atorsorfor something called thesandpile group.Remarkably, for a graph embedded in a plane, the samesandpile torsorhas been rediscovered many times using seemingly distinct constructions. It has been a long term goal of mine to better understand what is so special about this particular structure. In joint work with Ganguly, we make precise a sense in which thistorsorstructureis canonical in terms of a contraction-deletion property calledconsistency.I will also discuss ongoing work with Ding, Tóthmérész, and Yuen to generalize the consistency result to arbitraryribbon graphsandoriented regular matroids.