Periods of connections and special values of the gamma function

Speaker: Javier Fresan, Max Planck Institute for Mathematics, Bonn

The Lerch-Chowla-Selberg formula expresses the periods of an elliptic curve with complex multiplication as a product of special values of the Gamma function. Motivated by a new proof of this result, Gross conjectured at the end of the 70s that the same holds for any geometric Hodge structure with complex multiplication by an abelian field. Work of Gross, Deligne, Anderson, Colmez and, more recently, Maillot and Rössler settled several cases of the conjecture. In this talk I will explain a different approach, based on a product formula, by Saito and Terasoma, for the periods of flat connections whose local system of horizontal sections are equipped with a rational structure.