Weak Maass forms and mock modular forms

Over the last decade, there has been a surge of research pertaining to “weak Maass forms”, certain non-holomorphic modular forms, and “mock modular forms”, relatives of S. Ramanujan’s original “mock theta functions”. In this talk we offer an introduction to this theory, emphasizing contributions of K.
Ono, S. Zwegers, and collaborators. As an application, we will discuss joint work with Ono regarding basic hypergeometric series and the question of modularity.