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Explore Maass operators in integral weight through this 1 hour 19 minute conference talk delivered at the International Centre for Theoretical Sciences. Delve into the mathematical framework of Maass operators as they apply to integral weight modular forms, building upon the foundational concepts of harmonic Maass forms and mock modular forms. Learn how these operators function within the broader context of modular form theory and their significance in number theory applications. Examine the technical aspects of integral weight cases and their relationship to the holomorphic and non-holomorphic components of harmonic Maass forms. Discover the connections between Maass operators and the mathematical structures that emerged from Ramanujan's original work on mock theta functions, now understood through the lens of modern harmonic analysis. Gain insights into how these operators contribute to current research in partition theory, representation theory, and their applications in theoretical physics, particularly in understanding the modular properties that make these mathematical objects so powerful across diverse areas of mathematics.
