S. Ghazouani - Isoholonomic foliations of moduli spaces of Riemann surfaces

Selim Ghazouani , Fanny Bastien (1) , Donovan Humphries (1)

1 IF - Institut Fourier

In this talk, I will introduce families of foliations on the moduli space of Riemann surfaces M_{g,n} which we call Veech foliations. These foliations are defined by identifying M_{g,n} to certain moduli spaces of flat structures and were first defined by Bill Veech. I will try to expose their specificities, both of geometric and dynamical nature. If time permits I will try to illustrate how the case g=1 is linked to certain differential equations whose solutions are special functions of distinguished interest. This is joint work with Luc Pirio.

Mots clés: Foliations and algebraic geometry; isoholonomic foliations; moduli spaces; Riemann surfaces

Mots clés: eem2019; Grenoble; Feuilletages et géométrie algébrique

Domaines: Mathématiques [math]

Selim Ghazouani, Fanny Bastien, Donovan Humphries. S. Ghazouani - Isoholonomic foliations of moduli spaces of Riemann surfaces: Summer School 2019 - Foliations and algebraic geometry. 2019. ⟨medihal-02274892⟩