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Residual Distribution of Modular Symbols and Other Types of Cohomology Classes

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Speaker: 
Asbjørn Nordentoft
Affiliation: 
Universität Bonn
Date: 
Wed, 2020-11-11 14:30 - 15:30
Parent event: 
Number theory lunch seminar

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

 In 2016 Mazur and Rubin put forth a number of conjectures concerning the arithmetic
distribution of modular symbols motivated by certain questions in Diophantine stability. One of these conjectures  predicts that (appropriately normalized) modular symbols should equidistribute modulo a prime. In this talk I will present a proof of an  average version of this conjecture using twisted Eisenstein series. A different proof was given independently by Lee and  Sun using dynamical methods. Our automorphic proof has a number of advantages; it allows for a joint equidistribution result and (most importantly) generalizes to classes in the first cohomology of arithmetic subgroups of $\mathrm{SO}(n,1)$. In certain special
 cases we can actually prove the full conjecture using connections to Eisenstein congruences.

All this is joint work with Petru Constantinescu (UCL).

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