Speaker: Riad Masri (Texas A&M University)
Title: Harmonic weak Maass forms and partition ranks
Abstract: The rank of an integer partition is the largest part minus the number of parts. The notion of rank was introduced by Freeman Dyson to give a combinatorial explanation of Ramanujan’s famous partition congruences. Recent developments in the theory of harmonic weak Maass forms have led to new exact formulas for partition ranks. I will explain how these formulas can be combined with analytic methods to give asymptotics for partition ranks with power saving error terms.