Research

Research interests: I usually work on problems involving geometric structures on surfaces and 3-manifolds.

I have a special interest for hyperbolic geometry, so my motivation often comes from the connections with one of the following topics: 

• Hyperbolic surfaces and hyperbolic 3-manifolds

• Kleinian groups

• (Higher) Teichmüller theory

Preprints

• Topological and geometric restrictions on hyperconvex representations arXiv PDF
  with James Farre and Beatrice Pozzetti

• Entropy, volume, and diameter in SO(p,q+1)-higher Teichmüller spaces arXiv PDF
  with Filippo Mazzoli

• Hyperbolic Heegaard splittings and Dehn twists arXiv PDF
  with Peter Feller and Alessandro Sisto 

• Divisible convex sets with properly embedded cones arXiv PDF
  with Pierre-Louis Blayac 

• Uniform models and short curves for random 3-manifolds arXiv PDF
  with Peter Feller and Alessandro Sisto

Publications

• SO(2,n+1)-maximal representations and hyperbolic surfaces arXiv PDF
  with Filippo Mazzoli
  To appear in Memoirs of the AMS

• Length functions in Teichmüller and anti de Sitter geometry Journal PDF
  with Filippo Mazzoli
  Forum of Mathematics, Sigma 11 (2023), e101 1-37

• Small eigenvalues of random 3-manifolds Journal PDF
  with Ursula Hamenstädt
  Transactions of the AMS 375 (2022), 3795-3840

• Volumes of random 3-manifolds Journal PDF
  Journal of Topology 14 (2021), 504-537