Combinatorics Seminar: Hyperplane arrangements and shuffling cards

Jason Fulman, USC

Title: Hyperplane arrangements and shuffling cards

Abstract: Bidigare, Hanlon, and Rockmore discovered a combinatorial notion of random walk on the chambers of a real hyperplane arrangement. Their construction includes shuffling methods such as the top to random shuffle and ordinary riffle shuffling. They obtain a combinatorial formula for the eigenvalues of the transition matrix of these Markov chains, which turn out to have all eigenvalues real despite being non-symmetric. There are also a number of extensions (random walk on oriented matroids, buildings, and left-regular bands).