On the distribution of modular symbols and cohomology classes

Appears in collection : Summer School 2022 - Cohomology, Geometry and Explicit number theory (COGENT)

Motivated by a series of conjectures of Mazur, Rubin and Stein, the study of the arithmetic statistics of modular symbols has received a lot of attention in recent years. In this talk, I will highlight several results about the distribution of modular symbols, including their Gaussian distribution and the residual equidistribution modulo p. I will also discuss about generalisations to cohomology classes in higher dimensions. Part of this talk is joint work with Asbjørn Nordentoft.