I am generally interested in hyperbolic geometry and low dimensional topology, with focus mainly on the study of geometric structures on surfaces. Currently, my research centres on Teichmüller theory around a deformation called grafting. In its simplest form, grafting is the insertion in a hyperbolic surface of a flat cylinder in place of a simple closed geodesic. But it appears also in different flavours, for instance as deformation of complex projective structures, or deformation of Hitchin representations.

Geometric objects I often use in my work are hyperbolic surfaces, translation surfaces, geodesic currents, length functions, train tracks, measured laminations and foliations.

I also would like to learn more about higher Teichmüller theory and how some of the concepts and tools developed in the classical theory can be generalized in the setting of Hitchin representations.

• A geometric boundary for the moduli space of grafted surfaces arXiv:2411.04921 

• Geometry and dynamics of Hitchin grafting representations (with Pierre-Louis Blayac, Ursula Hamenstädt and Théo Marty) arXiv:2407.07748

Here you can find my Master thesis, which presents a result by Maryam Mirzakhani from 2008.

Master Thesis - Earthquake and horocycle flows over Teichmuller space
Advisor: Bruno Martelli