Tropical structures in sandpile groups and convex domains
Date:
Wednesday, March 8, 2017 13:45 - 15:45
Speaker:
Mikhail Shkolnikov (University of Geneva)
Location:
Mondi Seminar Room 2, Central Building
Series:
Mathematics and CS Seminar
Host:
Tamas Hausel
Contact:
DE ANTONI Jessica
It was observed experimentally that a small perturbation of a maximal sandpile on a big convex portion of a lattice deviates from the maximum along a thin balanced graph. The reason for that is the existence of certain scaling limit of the model. The limiting model is continuous and can be described in terms of dynamics on tropical analytic functions vanishing at the boundary of the corresponding convex domain. The fundamental solution of the model is a curve with an infinite number of punctures which appears to be a complete invariant of the domain.