Mathematics Colloquia and Seminars

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I will present a proof, discovered recently by myself and Anton Mellit, of the well-studied "shuffle conjecture" of Haglund, Haiman, Loehr, Remmel, and Ulyanov, which predicts the character of the ring of diagonal coinvariants in 2n variables in terms of some very subtle combinatorics. This topic has since been generalized in many fascinating directions, and has found connections to knot invariants, DAHAs, and the cohomology of affine springer fibers, due to several authors. I'll explain the conjecture as well as the new algebraic structures that arise in this proof, and hopefully I will also have time to explain some desirable future directions.