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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