Automorphic Forms, Mock Modular Forms and String Theory (17w5097)
Daniel Persson (Chalmers University of Technology)
Terry Gannon (University of Alberta)
David Ginzburg (Tel Aviv University)
Axel Kleinschmidt (Max Planck Institute for Gravitational Physics)
Stephen Miller (Rutgers University)
Boris Pioline (CERN)
Specifically, the workshop will focus on the following cross-disciplinary areas:
• The connection between string theory amplitudes and small automorphic representations. The most supersymmetric string theory scattering processes have been interpreted as very small auto- morphic representations. Less supersymmetric processes call for an in-depth study of increasingly larger automorphic representation.
• Representation theoretic aspects of mock modular forms. Classical modular forms have a natural interpretation in terms of representation theory of reductive groups. What about mock modular forms?
• Automorphic forms on Kac-Moody groups and their relation with string amplitudes in low dimensions. The theory of automorphic forms on Kac-Moody groups and especially their Fourier ex- pansion needs to be developed further for understanding low-dimensional string theory amplitudes.
• Mock modular forms and Siegel modular forms in umbral moonshine. Umbral moonshine gives rise to a rich family of Jacobi forms and mock modular forms. Jacobi forms can be lifted to Siegel modular forms. What is the corresponding lift of the associated mock modular forms?
• Connections between umbral moonshine and Calabi-Yau compactifications of string theory. A proper string theory understand- ing of Mathieu or umbral moonshine in terms of a an underlying con- formal field theory is currently lacking.
• Automorphic representations and black hole counting. Understanding the microscopic origin of the entropy of a black hole requires counting black hole states in string theory. Since the same states also contribute to the Fourier expansion of automorphic forms, the counting problem could be rephrased in automorphic terms.