We construct a compactification of the moduli spaces of abelian differentials on Riemann
surfaces with prescribed zeroes and poles. This compactification, called the moduli space of …

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We review the different notions of translation surfaces that are necessary to understand
McMullen's classification of GL 2+(ℝ)-orbit closures in genus two. We start by recalling the …

This paper investigates the interaction between Teichmüller theory and algebraic geometry
mediated by Hodge theory and periods. Its main goal is to present several remarkable …

For the moduli spaces of Abelian differentials, the Euler characteristic is one of the most
intrinsic topological invariants. We give a formula for the Euler characteristic that relies on …

A translation surface is a multifaceted object that can be studied with the tools of dynamics,
analysis, or algebraic geometry. Moduli spaces of translation surfaces exhibit equally rich …

We propose a unifying setting for dealing with monodromically atypical intersections that
goes beyond the usual Zilber-Pink conjecture. In particular we obtain a new proof of …

Let Γ be a lattice in SO_0(n,1). We prove that if the associated locally symmetric space
contains infinitely many maximal totally geodesic subspaces of dimension at least 2, then Γ …

We provide numerical evidence that the GL 2 (R)-orbit closure of the unfolding of the (3, 4,
13)-triangle in the moduli space of Abelian differentials is a previously unknown 4 …

We show that the partial compactification of a stratum of Abelian differentials previously
considered by Mirzakhani and Wright is not an algebraic variety. Despite this, we use a …