Automorphic Structures in String Theory: March 4 – 8, 2019

 

 

Organized by Terry Gannon, David Ginzburg, Axel Kleinschmidt, Stephen D. Miller, Daniel Persson, Boris Pioline

 

The purpose of this interdisciplinary workshop is to investigate connections between string theory, automorphic forms, mock modular forms, and beyond.
Automorphic representations are part of the basic language of the Langlands program, while at the same time playing a crucial role in understanding the structure of scattering amplitudes in string theory. Mock modular forms appear ubiquitously in studying quantum black holes and new moonshine phenomena. Investigations of string amplitudes have also given rise to new objects called “modular graph functions”, whose mathematical structure is only beginning to emerge. Higher-curvature corrections in string theory satisfy unconventional (“Poisson-type”) differential equations that call for a generalization of the notion of automorphic form that goes beyond the current mathematical framework. The workshop represents the kick-off event for a month-long program with the same title, and therefore aims to introduce the various topics and open questions, which can then be further discussed and fostered during the program. Since the participants will come from a wide range of different fields the workshop will combine research talks with longer introductory lectures by physicists for mathematicians, and vice versa. This may be viewed as a continuation of the workshops on “Automorphic forms, mock modular forms and string theory”, which ran at SCGP in the fall of 2016 and at BIRS in the fall of 2017.