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Online: Extended modularity and deformations of Riemann surfaces

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Gabriele Bogo
Wed, 2020-09-02 14:30 - 15:30
Parent event: 
Number theory lunch seminar

Modular forms appear in Poincaré's work as solutions of second order linear ODEs defined on hyperbolic Riemann surfaces. These differential equations, called uniformizing ODEs, were classically related to the study of the universal cover of (hyperbolic) Riemann surfaces.

In this talk I will discuss certain functions arising as solutions of "perturbed" uniformizing ODEs. These "perturbed" ODEs are related to the deformation of the complex structure of a given Riemann surface. It turns out that their solutions can be described in terms of quasimodular forms and Eichler integrals.
In the second part of the talk, a description of these objects in terms of extensions of symmetric tensor representations and vector-valued modular forms will be given. This leads to the definition of a new class of functions called extended modular forms; if time permits I will discuss the basic definitions and present some examples.

Zoom Online Meeting ID: 919 6497 4060
For password see the email or contact Pieter Moree (moree@mpim...).

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