Examples of Harmonic Maass Forms of Integral Weight by Michael Griffin

Discussion Meeting: Harmonic Maass Forms, Mock Modular Forms and Their Applications

ORGANIZERS: Ajit Bhand (IISER Bhopal, India) and Karam Deo Shankhadhar (IISER Bhopal, India)
DATE & TIME: 30 June 2025 to 04 July 2025
VENUE: Madhava Lecture Hall

Modular forms and their various generalizations are ubiquitous in mathematics. They enjoy diverse and often surprising applications in many areas of mathematics, including number theory, representation theory, discrete geometry as well as theoretical physics.

In his deathbed letter to G. H. Hardy, written in 1920, Ramanujan described, what he called, mock theta functions which have “modular-like" properties. These mysterious functions were not completely understood until Zwegers as well as Bruinier and Funke discovered the correct mathematical framework to study them. We now know that Ramanujan’s mock theta functions are the holomorphic parts of certain nonholomorphic functions called harmonic Maass forms. Both harmonic Maass forms and mock modular forms have applications in many diverse areas such as partition theory, elliptic curves, black hole physics and representation theory.

Harmonic Maass forms and mock modular forms have been active areas of research in the last 25 years. The broad goal of this discussion meeting is to bring experts in the field to deliver lectures on the foundational aspects of this subject and to discuss some of the recent results and applications. We hope that this discussion meeting will generate greater interest, appreciation and excitement for harmonic Maass forms and mock modular forms among students and active researchers in mathematics and theoretical physics in India.


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PROGRAM LINK
https://icts.res.in/discussion-meetin...