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Alexander Lazar: Shuffle Theorems and Sandpiles

Speaker: Alexander Lazar (Université Libre de Bruxelles)

Time: Wed 2024-09-11 10.15 - 11.15

Location: 3418

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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.