Mock Theta Functions in the Context of Harmonic Maass Forms

Explore mock theta functions within the framework of harmonic Maass forms in this one-hour conference talk delivered at the International Centre for Theoretical Sciences. Delve into the mathematical concepts that originated from Ramanujan's deathbed letter to G.H. Hardy in 1920, where he described mysterious functions with "modular-like" properties that remained poorly understood for decades. Learn how modern mathematical frameworks developed by Zwegers, Bruinier, and Funke revealed that Ramanujan's mock theta functions are actually the holomorphic parts of nonholomorphic functions called harmonic Maass forms. Discover the connections between these mathematical objects and their applications across diverse fields including partition theory, elliptic curves, black hole physics, and representation theory. Gain insights into how harmonic Maass forms and mock modular forms have become active research areas over the past 25 years, building upon the foundational work that finally provided the correct mathematical context for understanding Ramanujan's enigmatic functions. This presentation is part of a broader discussion meeting focused on harmonic Maass forms, mock modular forms, and their wide-ranging applications in mathematics and theoretical physics.