Research

I am interested in low dimensional topology. In particular I have been studying hyperbolic 3-manifolds with non-finitely generated fundamental group. I am also interested in higher Teichmüller Theory and counting problems on surfaces.

Papers:

1. A locally hyperbolic 3-manifold that is not hyperbolic, Proc. Amer. Math. Soc. 146 (2018), 5475-5483.
2. Discrete groups without finite quotients with Juan Souto, Topology and its Applications, 2018, Vol.248, pp.138-142.
3. Hyperbolicity of links complements in Seifert fibered spaces with José Andrés Rodríguez Migueles, Algebraic and Geometry Topology in 2020.
4. A locally hyperbolic 3-manifold that is not homotopy equivalent to any
   hyperbolic 3-manifold, Conform. Geom. Dyn. 24 (2020), 118-130.
5. Hyperbolic limits of Cantor set complements in the sphere with Franco Vargas Pallete; Bulletin of the London Mathematical Society, 2022.
6. On volumes and filling collections of multicurves with José Andrés Rodríguez Migueles and Andrew Yarmola; Fall 2020 pre-print, accepted at the Journal of Topology.

Pre-Prints: 

1. Hyperbolization of infinite type 3-manifolds; April 2019 pre-print, submitted.
2. Volume bounds for the canonical lift complement of a random geodesic, joint work Yannick Krifka, Didac Martinez-Granado , Franco Vargas Pallete Summer 2021 pre-print, submitted.
3. Effective contraction of skinning maps, joint work with Lorenzo Dello Schiavo, Fall 2021 pre-print, submitted.

Collaborators:

• Juan Souto
• José Andrés Rodrigues Migueles
• Andrew Yarmola
• Dídac Martínez-Granado
• Franco Vargas Pallete
• Yannick Krifka
• Lorenzo Dello Schiavo