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.
- 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, accepted for publication on Algebraic and Geometry Topology in 2020.
- A locally hyperbolic 3-manifold that is not homotopy equivalent to any
hyperbolic 3-manifold, Conform. Geom. Dyn. 24 (2020), 118-130.
- Hyperbolization of infinite type 3-manifolds; April 2019 pre-print, submitted.
- On volumes and filling collections of multicurves with José Andrés Rodríguez Migueles and Andrew Yarmola; Fall 2020 pre-print, submitted.
- Hyperbolic limits of Cantor set complements in the sphere with Franco Vargas Pallete; Spring 2020 pre-print, submitted.