Summation Formulas - From Classical Foundations to Harmonic Maass Forms

Explore the evolution of summation formulas from their classical origins to their modern connections with harmonic Maass forms in this 55-minute conference talk. Delve into the mathematical journey that traces how traditional summation techniques have developed into sophisticated tools for understanding harmonic Maass forms and mock modular forms. Learn about the foundational principles underlying these mathematical structures and discover how classical summation methods provide insights into these advanced areas of number theory. Examine the theoretical frameworks that connect historical mathematical concepts with contemporary research in modular forms and their generalizations. Gain understanding of how summation formulas serve as bridges between classical mathematics and modern developments in harmonic analysis, particularly in the context of Ramanujan's mock theta functions and their relationship to harmonic Maass forms.