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 December 2017, published in PAMS.
  2. Discrete groups without finite quotients with Juan Souto, April 2018, published in Topology and its Applications.
  3. Hyperbolicity of links complements in Seifert fibered spaces with José Andrés Rodríguez Migueles, December 2019, accepted for publication on AGT.
  4. A locally hyperbolic 3-manifold that is not homotopy equivalent to any
    hyperbolic 3-manifold, December 2018, pre-print, submitted.
  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: