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:
- A locally hyperbolic 3-manifold that is not hyperbolic, Proc. Amer. Math. Soc. 146 (2018), 5475-5483.
- Discrete groups without finite quotients with Juan Souto, Topology and its Applications, 2018, Vol.248, pp.138-142.
- Hyperbolicity of links complements in Seifert fibered spaces with José Andrés Rodríguez Migueles, December 2019, accepted for publication on Algebraic and Geometry Topology.
- 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.
- Hyperbolization of infinite type 3-manifolds; April 2019, pre-print, submitted.
- On volumes and filling collections of multicurves; Fall 2019, pre-print, submitted.
- Deformation Spaces of Infinite type 3-manifolds; in preparation.
- Density of Cantor Sets Complements with Franco Vargas Pallete; in preparation.