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:

  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, accepted for publication on 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.

Pre-Prints:

  1. Hyperbolization of infinite type 3-manifolds; April 2019 pre-print, submitted.
  2. On volumes and filling collections of multicurves with José Andrés Rodríguez Migueles and Andrew Yarmola; Fall 2020 pre-print, submitted.
  3. Hyperbolic limits of Cantor set complements in the sphere with Franco Vargas Pallete; Spring 2020 pre-print, submitted.

Collaborators: