Durfee symbol congruences and weak Maass forms

Andrews defined k-marked Durfee symbols as an infinite family of combinatorial objects that generalize partitions, and arise naturally in the study of moments of Dyson's partition rank. He also defined the smallest parts partition function, which is connected to moments for the rank and Dyson's partition crank. He then proved Ramanujan-type congruences for both Durfee symbols and the smallest parts partition function. This talk explains these results from an analytic perspective, showing that the generating functions are natural examples of quasi-mock theta functions (which come from differentiating weak Maass forms). It is of particular interest that the modular weight of these functions grows with k, in contrast with the fact that known examples of hypergeometric Maass forms have weight at most 3/2. Another notable corollary is that the Durfee symbols and smallest parts partition function satisfy infinite families of congruences, similar to those that have recently been shown for the crank and rank.