Statistics for Unimodal Sequences

Date: 29/03/2023
Time: 14:00 - 15:30

Location: RISC castle, Hagenberg

Unimodal sequences generalize integer partitions and are prevalent throughout mathematics, but until recently, comparatively less was known about their large statistical behavior. We give an overview of probabilistic techniques used to study integer partitions and their adaptation to unimodal sequences; this relates to limit-shapes and distributions part sizes. We then apply new developments in the theory of automorphic forms to prove precise asymptotic series for the rank of unimodal sequences. This is joint work with Kathrin Bringmann.