The algebraic hull of the Kontsevich–Zorich cocycle Page 1 Annals of Mathematics 188 (2018),
281–313 https://doi.org/10.4007/annals.2018.188.1.5 The algebraic hull of the Kontsevich–Zorich …

We prove that invariant subbundles of the Kontsevich-Zorich cocycle respect the Hodge
structure. In particular, we establish a version of Deligne semisimplicity in this context. This …

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 describe all the situations in which the Kontsevich–Zorich (KZ) cocycle has zero
Lyapunov exponents. Confirming a conjecture of Forni, Matheus, and Zorich, we find this …

The variations of Hodge structures of weight one associated to square-tiled surfaces
naturally generate interesting subgroups of integral symplectic matrices called Kontsevich …

The classical wind-tree model corresponds to a billiard in the plane endowed with Z2-
periodic obstacles of rectangular shape; the sides of the rectangles are aligned along the …

We compute the Zariski closure of the Kontsevich–Zorich monodromy groups arising from
certain square-tiled surfaces that are geometrically motivated. Specifically we consider three …

For all $ d $ belonging to a density-$1/8$ subset of the natural numbers, we give an
example of a square-tiled surface conjecturally realizing the group $\mathrm {SO}^*(2d) $ in …

This book is a remarkable contribution to the literature on dynamical systems and geometry.
It consists of a selection of work in current research on Teichmüller dynamics, a field that has …

Ce travail s' inscrit dans le cadre de la dynamique de Teichmüller, un domaine riche dont les
techniques combinent des méthodes provenant de l'analyse complexe, la géométrie di …