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).
Links:
[1] http://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/de/node/246