Lucien Clavier

Ph.D. (2016) Cornell University

First Position

Consultant in Capital Markets, Financial Risk at Deloitte Luxembourg

Dissertation

Non-affine horocycle orbit closures on strata of translation surfaces: new examples

Advisor

John Smillie

Research Area

Dynamics on Moduli spaces of flat surfaces.

Abstract

We investigate specific examples of locally-defined real vector-fields on strata of translation surfaces. Integrating SL(2,$\mathbb{R}$)-loci of Veech surfaces along these vector-fields yield interesting new examples of horocycle-invariant ergodic measures. These measures are supported on closed immersed manifolds with boundary that approach the boundary of strata in a novel way.