Cycle Integrals of the j-function by Duke, Imamoglu, and Toth

Explore cycle integrals of the j-function through the groundbreaking work of Duke, Imamoglu, and Toth in this conference talk delivered at the International Centre for Theoretical Sciences. Delve into advanced topics in modular forms theory as part of a comprehensive discussion meeting on harmonic Maass forms, mock modular forms, and their applications. Examine the mathematical framework surrounding these cycle integrals and their significance in the broader context of modular forms research. Learn about the connections between the j-function and various mathematical structures, building upon the foundational work that has shaped our understanding of mock theta functions since Ramanujan's original discoveries. Gain insights into how these mathematical concepts apply across diverse areas including number theory, representation theory, discrete geometry, and theoretical physics. Understand the evolution of this field from Ramanujan's mysterious mock theta functions to the modern framework established by researchers like Zwegers, Bruinier, and Funke, and discover how harmonic Maass forms provide the proper context for understanding these mathematical objects.