Generalization of Monster Denominator Identity to Higher Level Using Harmonic Maass Forms

Explore the mathematical generalization of the Monster Denominator Identity to higher levels through harmonic analysis in this 54-minute conference talk. Delve into advanced concepts connecting modular forms, harmonic Maass forms, and their applications in number theory and representation theory. Learn how the Monster Denominator Identity, a fundamental result in the theory of monstrous moonshine, can be extended to more general settings using harmonic techniques. Examine the mathematical framework that bridges classical modular forms with their modern generalizations, including mock modular forms and harmonic Maass forms. Discover the connections between these mathematical objects and their applications in diverse areas such as partition theory, elliptic curves, and theoretical physics. Gain insights into current research developments in this active area of mathematics that has seen significant progress over the past 25 years, building upon foundational work by mathematicians like Ramanujan, Zwegers, Bruinier, and Funke.