Seminar - Zachary Hamacker

Thursday, June 9, 2022 1:00 pm - 1:00 pm EDT (GMT -04:00)

Title: Virtual characters of permutation statistics

Speaker: Zachary Hamacker
Affiliation: University of Florida
Room: MC 5483


Functions of permutations are studied in a wide variety of fields including probability, statistics and theoretical computer science. I will introduce a method for studying such functions using representation theory and symmetric functions. As a consequence, one can extract detailed information about asymptotic behavior of many permutation statistics with respect to non-uniform measures that are invariant under conjugation. The key new tool is a combinatorial formula called the path Murnaghan-Nakayama rule that gives the Schur expansion of a novel basis of the ring of symmetric functions. This is joint work with Brendon Rhoades.