2.00 pm, Lecture Hall 804
Modular Symmetry and its Taller Cousins
Madhusudan Raman
TIFR, Mumbai.
24-09-19

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Abstract

Motivated by their appearance in the study of resurgence, supersymmetric gauge theories, and string theory, we study the relations governing quasi-automorphic forms associated to certain discrete subgroups of SL(2,R) called Hecke groups. We will begin with a brief review of our motivations from physics, and follow that with a discussion of the modular group and structures associated to it: Eisenstein series, the Ramanujan identities, elliptic curves, and the Chazy equation. We then discuss generalisations of each of these objects/structures to an infinite family of subgroups of SL(2,R) called Hecke groups. Along the way, we will remark on similarities between the intuition behind these constructions and techniques from the literature on supersymmetric gauge theories. We will end with some comments on future directions for research.

The prerequisites are minimal, and the talk will be pedagogical in nature. This is work done in collaboration with Sujay Ashok (IMSc) and Dileep Jatkar (HRI).