A significant obstacle for quantum field theory is incorporating gravity, and a proposed solution to this challenge is to use oscillating strings to model gravitons. In this framework, understanding graviton behaviour involves analyzing certain functions on moduli spaces. These functions often arise as automorphic forms. For example, when calculating string scattering amplitudes for the 4-graviton, solutions to certain differential equations involving automorphic functions appear as coefficients. The first few solutions to these differential equations are known on SL_2(Z). We aim to find an analogous spectral solution on SL_3(Z). In this talk, we'll discuss some of the tools used to find such solutions on SL_2(Z), along with specific challenges (and possible resolutions) in extending them to the SL_3(Z) case. This talk is based on work in progress joint with Holley Friedlander, Kim Klinger-Logan, Manish Pandey, and Runqiu Xu.
Automorphic forms and string scattering amplitudes
Maryam Khaqan, University of TorontoAuthors: Maryam Khaqan, Holley Friedlander, Kim Klinger-Logan, Manish Pandey, and Runqiu Xu.
2023 AWM Research Symposium
Rethinking Number Theory [Organized by Deewang Bhamidipati, Eva Goedhart, and Amita Malik]