Research
Research interests
I usually work on problems involving geometric structures on surfaces and 3-manifolds. I have a special interest in hyperbolic geometry, so my motivation often comes from connections with one of the following topics:
- Hyperbolic surfaces and hyperbolic 3-manifolds
- Kleinian groups
- (Higher) Teichmüller theory
Preprints
- Linear volume bounds for drilling and filling arXiv, PDF
- Geometric components of representation spaces via robust families of submanifolds arXiv, PDF
- Effective length-projection bounds for hyperbolic 3-manifolds diffeomorphic to SxR arXiv, PDF
-
Effective hyperbolization and length bounds for Heegaard splittings
arXiv,
PDF
with Peter Feller and Alessandro Sisto -
Geometry of hyperconvex representations of surface groups
arXiv,
PDF
with James Farre and Beatrice Pozzetti -
Hyperbolic Heegaard splittings and Dehn twists
arXiv,
PDF
with Peter Feller and Alessandro Sisto
Publications
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Topological and geometric restrictions on hyperconvex representations
Journal,
PDF
with James Farre and Beatrice Pozzetti
Crelle's Journal 827 (2025), 227-251 -
Entropy, volume, and diameter in SO(p,q+1)-higher Teichmüller spaces
Journal,
PDF
with Filippo Mazzoli
Commentarii Mathematici Helvetici, online first -
Divisible convex sets with properly embedded cones
Journal,
PDF
with Pierre-Louis Blayac
Publications Mathématiques de l'IHÉS 141 (2025), 99-189 -
Uniform models and short curves for random 3-manifolds
Journal,
PDF
with Peter Feller and Alessandro Sisto
Compositio Mathematica 161 (2025), 447-502 -
SO(2,n+1)-maximal representations and hyperbolic surfaces
Journal,
PDF
with Filippo Mazzoli
Memoirs of the AMS 313 (2025), no. 1587 -
Length functions in Teichmüller and anti-de Sitter geometry
Journal,
PDF
with Filippo Mazzoli
Forum of Mathematics, Sigma 11 (2023), e101 -
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