# Jim Haglund: Three Faces of the Delta Conjecture

**Time: **
Wed 2019-05-22 10.15 - 11.15

**Lecturer: **
Jim Haglund, University of Pennsylvania

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

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.