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Explore the profound mathematical legacy of Srinivasa Ramanujan and the modern development of modular forms in this conference lecture delivered at the International Centre for Theoretical Sciences. Delve into the fascinating story of Ramanujan's deathbed letter to G.H. Hardy in 1920, where he described mysterious "mock theta functions" with modular-like properties that remained enigmatic for decades. Discover how these functions were finally understood through the groundbreaking work of Zwegers, Bruinier, and Funke, who revealed that Ramanujan's mock theta functions are actually the holomorphic parts of nonholomorphic functions called harmonic Maass forms. Learn about the diverse applications of both harmonic Maass forms and mock modular forms across multiple mathematical disciplines, including partition theory, elliptic curves, black hole physics, and representation theory. Gain insight into how these mathematical objects have become active areas of research over the past 25 years, connecting number theory, representation theory, discrete geometry, and theoretical physics in surprising ways. Understand the foundational aspects of this subject and appreciate the continuing influence of Ramanujan's mathematical intuition on contemporary research in modular forms and their generalizations.
