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 Teichmuller Theory and counting problems on surfaces.

Here is my research statement.

Papers and pre-prints:

  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, December 2019, accepted for publication on Algebraic and Geometry Topology.
  4. A locally hyperbolic 3-manifold that is not homotopy equivalent to any
    hyperbolic 3-manifold, December 2018, pre-print, accepted for publication in Conformal Geometry and Dynamics.
  5. Hyperbolization of infinite type 3-manifolds; April 2019, pre-print, submitted.
  6. On volumes and filling collections of multicurves; Fall 2019, pre-print, submitted.
  7. Deformation Spaces of Infinite type 3-manifolds; in preparation.
  8. Density of Cantor Sets Complements with Franco Vargas Pallete; in preparation.

Collaborators: