Eichler-Selberg Relations for Traces of Singular Moduli

Explore the mathematical connections between Eichler-Selberg relations and traces of singular moduli in this 75-minute conference talk delivered by Ken Ono 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 intricate relationships between these mathematical objects and their significance in number theory, building upon the foundational work that connects Ramanujan's mock theta functions to modern harmonic Maass form theory. Gain insights into how Eichler-Selberg relations provide a framework for understanding traces of singular moduli, contributing to the broader understanding of modular-like properties in mathematics. Learn from expert analysis of these sophisticated mathematical structures and their applications across diverse areas including partition theory, elliptic curves, and representation theory.