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Chip-firing on graphs and the geometry of Riemann surfaces

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If you have a question about this talk, please contact Yaël Dillies.

I will discuss a parallel between two seemingly disparate worlds: Riemann surfaces, which are objects of complex analysis, and finite graphs, which are objects of combinatorics. Often, a structure on the geometric side suggests an analogous structure on the combinatorial one. I will illustrate this principle in one very pleasant example, where the combinatorial structure is known as “chip firing”. While the link between the worlds is technical and still somewhat mysterious, it is powerful enough to allow one to use combinatorics to deduce geometric consequences. I’ll discuss some of the advances that these tools have brought us in recent years.

This talk is part of the The Archimedeans series.

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