We will show that the Ceresa cycles of Fermat curves of prime degree greater than 7 are of infinite order modulo rational equivalence (i.e. in the Chow group). The proof combines several results due to B. Harris, Pulte, Kaenders and Darmon-Rotger-Sols on the arithmetic and geometry of the mixed Hodge structure on the space of quadratic iterated integrals on an algebraic curve with a result of Gross and Rohrlich on points of infinite order on Jacobians of Fermat curves. This is a joint work with V. Kumar Murty.

For the introductory slides on this topic, please see: http://www.fields.utoronto.ca/sites/default/files/uploads/pre-talk.pdf