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Explore the Hecke theory of harmonic Maass forms in this conference lecture delivered by Michael Griffin at the International Centre for Theoretical Sciences. Delve into the mathematical framework that connects Ramanujan's mysterious mock theta functions to modern harmonic Maass form theory, building upon the foundational work of Zwegers, Bruinier, and Funke. Learn how Hecke operators act on harmonic Maass forms and understand their role in the broader context of modular forms and their generalizations. Discover the connections between these mathematical objects and their applications across diverse fields including number theory, partition theory, elliptic curves, black hole physics, and representation theory. Gain insights into how harmonic Maass forms serve as the nonholomorphic extensions of Ramanujan's mock theta functions, providing the complete mathematical picture that eluded researchers for nearly a century after Ramanujan's deathbed letter to Hardy in 1920. This presentation forms part of a comprehensive discussion meeting focused on harmonic Maass forms, mock modular forms, and their wide-ranging applications in mathematics and theoretical physics.
