Description
Modularity describes a topic in the framework of arithmetic geometry which is the interplay of algebraic geometry and number theory. If a variety suits the requirements of being modular, it determines a modular form. From a physics perspective, modularity turns out to play an important role for the investigation of Calabi-Yau compactifications of string, M- or F-theory.
In this talk, I present an introduction to the framework of modularity and discuss its applications in the context of string-compactifications. In particular, I focus on the search for supersymmetric flux vacua of 3-dimensional M-theory compactified on Calabi-Yau fourfolds, arguing that modularity may serve as a sufficient condition for non-trivial fluxes. To strengthen its applicability, I demonstrate this arithmetic approach by presenting concrete examples.
