Mark Dukes (UCD)

will speak on

Symmetries in the sandpile model and the shuffle conjecture

Time: 2:00PM
Date: Wed 29th October 2025
Location: E0.32 (beside Pi restaurant) [map]

Abstract: In this talk we will present an overview of a collection of results from the last decade that concern unusual and unexpected symmetries in the Abelian sandpile model. Along the way we will meet several classes of bivariate polynomials, a new class of polyominos that we call sawtooth polyominos, and a new family of graphs termed clique-independent graphs. We will see how this work provides a combinatorial interpretation of some conjectured, and subsequently proven, results from algebraic combinatorics known as the shuffle conjecture.

(This talk is part of the Probability series.)

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