Speaker
Description
Modularity describes a phenomenon, where it is possible to assign a unique modular form to an algebraic variety by considering its number theoretical properties. As it turns out, modularity plays an important role for many physical applications involving Calabi-Yau geometries.
Based on the well-known results for flux compactifications of type IIB string theory compactified on modular Calabi-Yau threefolds, we discuss in this talk the application of modularity in the context of supersymmetric flux vacua of M-theory compactified on Calabi-Yau fourfolds. In particular, we argue that modularity may serve as a sufficient condition for non-trivial fluxes admitting suitable vacua.
Modularity can be tested by investigating the local zeta-function of the given variety. Introducing a deformation method for the efficient computation of (parts of) the zeta-function, we provide a technique to systematically search for modular points within a given family of fourfolds. To demonstrate the applicability of this method, we discuss an explicit modular example
This talk is based on joint work with H. Jockers and P. Kuusela [2312.07611].
