- Brendon Rhoades, University of California, San Diego
- The combinatorics, algebra, and geometry of ordered set partitions
- 09/20/2018
- 4:10 PM - 5:00 PM
- C304 Wells Hall
An {\em ordered set partition} of size $n$ is a set partition of $\{1, 2, \dots, n \}$ 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 $S_n$. We will discuss some combinatorial, algebraic, and geometric aspects of permutations (due to MacMahon, Carlitz, Chevalley, Steinberg, Artin, Lusztig-Stanley, Ehresmann, Borel, and Lascoux-Sch\"utzenberger). We will then describe how these results generalize to ordered set partitions and discuss a connection with the Haglund-Remmel-Wilson {\em Delta Conjecture} in the field of Macdonald polynomials. Joint with Jim Haglund, Brendan Pawlowski, and Mark Shimozono.