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Penn Mathematics Colloquium

Wednesday, April 4, 2018 - 3:30pm

Brendon Rhoades

UC San Diego

Location

University of Pennsylvania

DRL A2

Tea before the talk at 3pm in the math lounge, fourth floor DRL.

An ordered set partition of size n is a set partition of {1, 2, ... , n} with a specified order on its blocks. When the number of blocks equals the number of letters n, an ordered set partition is just a permutation in the symmetric group. We will discuss some combinatorial, algebraic, and geometric aspects of permutations (due to MacMahon, Carlitz, Chevalley, Steinberg, Artin, Garsia-Stanton, Lusztig-Stanley, Ehresmann, Borel, and Lascoux-Schutzenberger). We will then describe how these results generalize to ordered set partitions and discuss a connection with the Haglund-Remmel-Wilson Delta Conjecture in the field of Macdonald polynomials. Joint with Jim Haglund, Brendan Pawlowski, and Mark Shimozono.