Recent developments in sandpile models

Title

Recent developments in sandpile models

Speaker

Prof. Nikita Kalinin (GTIIT)

Time and Location

Apr. 27, 2023, Thursday, 18:30-19:30, E509 (Education Building, 5th floor)

Zoom link: https://gtiit.zoom.us/j/3343552026

Pizza will be provided after the colloquium

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. A relaxation of a sandpile state is defined as a sequence of topplings: if a vertex of valency k has at least k grains, then this vertex gives one grain to each of its neighbors, one repeats topplings while it is possible. Grains falling to sinks disappear.

Surprisingly for a certain initial state (“a small perturbation of the maximal stable state”), the final relaxed picture represents tropical curves and tropical hypersurfaces. I will explain definitions and show many beautiful pictures. We will discuss certain unexpected connections to number theory. Then I present results of an ongoing work about sandpile groups for infinite graphs.

Biography

PhD of the University of Geneva (2015).

Scientific interests: sandpile model, tropical geometry, knot theory, symplectic geometry, algebraic geometry.