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Tropical objects in sandpiles

  • Speaker:Nikita Kalinin (St. Petersburg State University)
  • TIME:March 2, 2023 20:00-21:00 Beijing time (15:00-16:00 St Petersburg time)
  • LOCATION:online

Recording: https://disk.pku.edu.cn:443/link/6E8BAFCA37E53DE67E20C4851B514234
Valid Until: 2027-04-30 23:59


Abstract: A sandpile model on a graph G is a simple cellular automata. A state of a sandpile model is a function from the vertices of G to non-negative integer numbers, representing the number of grains at each vertex of G. Then a relaxation of a sandpile model is defined as a sequence of topplings: if a vertex of valency k has at least k grains, then it gives one grain to each of its neighbors, one repeats topplings while it is possible.

Surprisingly for a certain initial state (“a small perturbation of the maximal stable state”), the final picture represents tropical curves and tropical hypersurfaces. I will explain all the definitions, show pictures and if time permits, we can speak about ideas in the proofs.


Bio: Nikita Kalinin is currently an associate professor at St. Petersburg State University. He graduated from St. Petersburg State University and obtained his PhD in mathematics at the University of Geneva. He was a senior scientific researcher at St. Petersburg Branch of the Higher School of Economics. Kalinin’s research interests include geometry, complex analysis, sandpiles, knots, number theory, graph theory etc. Nikita Kalinin was a gold medalist at IMO in 2005 and was awarded the Young Russian Mathematics grant and a Russian Science Foundation grant.