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Jim Haglund: Three Faces of the Delta Conjecture

Time: Wed 2019-05-22 10.15 - 11.15

Location: Room 3418, Lindstedtsvägen 25. Department of Mathematics, KTH

Participating: Jim Haglund, University of Pennsylvania

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Abstract: The Delta Conjecture says that a certain symmetric function, expressed in terms of Macdonald polynomial operators, equals a weighted sum over Dyck lattice paths. It contains the well-known Shuffle Theorem of Carlsson and Mellit as a special case. There is also a third side to the problem that has emerged, centered around the goal of showing the symmetric function side also has a representation-theoretic interpretation. We will overview some of this work, including a recent conjecture of Mike Zabrocki which says the two sides of the Delta Conjecture equal the bigraded character of a generalization of the diagonal coinvariant ring.