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Explore indefinite theta functions in this conference talk delivered by Michael Griffin at the International Centre for Theoretical Sciences. Delve into the mathematical framework of these specialized functions as part of a comprehensive discussion meeting on Harmonic Maass Forms, Mock Modular Forms and Their Applications. Learn about the theoretical foundations and properties of indefinite theta functions, which play a crucial role in understanding the broader landscape of modular forms and their generalizations. Discover how these functions connect to Ramanujan's mysterious mock theta functions and their relationship to harmonic Maass forms. Gain insights into the mathematical structures that have emerged from Ramanujan's deathbed letter to G.H. Hardy in 1920, where he first described mock theta functions with "modular-like" properties. Understand the modern mathematical framework developed by Zwegers, Bruinier, and Funke that finally provided complete understanding of these enigmatic functions. Examine the applications of indefinite theta functions across diverse mathematical areas including number theory, representation theory, discrete geometry, partition theory, elliptic curves, and theoretical physics, particularly in black hole physics.
