Mathematics Colloquia and Seminars

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Let S be the set of spanning trees of a given graph. Mathematicians have long been interested in calculating the cardinality of S. However, there is more to explore about S than just its cardinality, and I am particularly interested in the structure of this set.    This talk will focus on a concrete construction based on the rotor-routing algorithm which gives S a group-like structure. More precisely, we can understand S as a torsor for something called the sandpile group. Remarkably, for a graph embedded in a plane, the same sandpile torsor has 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 this torsor structure is canonical in terms of a contraction-deletion property called consistency. I will also discuss ongoing work with Ding, Tóthmérész, and Yuen to generalize the consistency result to arbitrary ribbon graphs and oriented regular matroids.