An abelian differential is a pair consisting of a smooth projective curve of genus g together with a non-zero algebraic 1-form. A stratum of abelian differentials is an algebraic orbifold that parametrizes abelian differentials such that the zeros of the 1-form have certain fixed multiplicities. In this talk, I will discuss the transcendence of the relative periods of abelian differentials, together with a characterization of the "least" transcendental ones and their distribution inside a stratum. On the geometric side, I will discuss the algebraic relations satisfied by the periods of an abelian differential when it varies inside an algebraic subvariety of a stratum. This is joint work with B. Klingler.
Speaker(s): Leonardo Lerer (Weizmann Institute)