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Speaker:

Gabriele Bogo
Affiliation:

SISSA, Trieste/MPIM
Date:

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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