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GeomTop Seminar: Talk by Mikhail Shkolnikov "Limit of the sandpile group"

Date: Wednesday, May 23, 2018 13:00 - 14:15
Speaker: Mikhail Shkolnikov
Location: Mondi Seminar Room 3, Central Building
Series: Formal Sciences Seminar
Host: Herbert Edelsbrunner
Contact: WAGNER Hubert

Abstract:

Title: Limit of the sandpile groupThe sandpile group is a finite abelian group defined for any graph. It is ofspecial interest for the piece of the lattice bounded by some convex domain. There arestrong indications that there is a limit for these groups when one fixes the domain andsends the mesh of the lattice to zero. Until recently, nobody was able tomake rigorous sense of this vague statement. Here is what we are suggesting: 1) for a given mesh, define a visual-type heuristic metric on the sandpile; 2) look at the persistence diagrams and whether they stabilise when mesh vanishes.
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