Alexander Lazar: Shuffle Theorems and Sandpiles

Abstract: Carlsson and Mellit's 2015 proof of the Compositional Shuffle Theorem established a combinatorial formula for the coefficients of the symmetric function \nabla e_n in terms of a certain class of labeled lattice paths. This result was a major breakthrough in what is still an active area of research within the combinatorial representation theory of the symmetric group. In this talk I will present recent work (joint with D'Adderio, Dukes, Iraci, Le Borgne, and Vanden Wyngaerd) in which we provide a new interpretation of this symmetric function in terms of the dynamics of the abelian sandpile model.