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Session S21 - Galois representations and automorphic forms

Wednesday, July 21, 16:50 ~ 17:30 UTC-3

Orthogonal modular forms, paramodular forms, and congruences

Gonzalo Tornaría

Universidad de la República, Uruguay   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

The goal of this talk is to explain how one can use orthogonal modular forms to find and prove congruences between paramodular forms.

In the first part of the talk I will give a brief review of orthogonal modular forms and how the case of SO(5) can be used to compute paramodular forms, based on recent work of Rama-T, Rösner-Weissauer, Dummigan-Pacetti-Rama-T.

In the second part of the talk I will explain how we use orthogonal modular forms to prove bi-congruences between paramodular forms as predicted by Golyshev. A key ingredient for this is the unexpected appearance of orthogonal eigenforms which /do not/ correspond to paramodular forms (see Rama-T in ANTS 2020).

Joint work with Gustavo Rama (Universidad de la República, Uruguay).

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