I am interested in low dimensional topology. In particular I have been studying hyperbolic low dimensional manifolds with nonfinitely generated fundamental group. I am also interested in higher Teichmüller Theory and counting problems on surfaces.
Papers:
 A locally hyperbolic 3manifold that is not hyperbolic, Proc. Amer. Math. Soc. 146 (2018), 54755483. In this paper we answer a question of Agol by showing that there exists a locally hyperbolic 3manifolds with no locally divisible subgroups that is not hyperbolic.
 Discrete groups without finite quotients with Juan Souto, Topology and its Applications, 2018, Vol.248, pp.138142. In this paper we build an exotic example of a nontrivial subgroup of isometry of hyperbolic 3space that has no nontrivial quotients. This corresponds to a hyperbolic 3orbifold. We also construct a hyperbolic 3manifold that is not residually finite.
 Hyperbolicity of links complements in Seifert fibered spaces with José Andrés Rodríguez Migueles, Algebraic and Geometry Topology in 2020. In this paper we give upper bounds for the volume of knots in Seifertfibered spaces based on the complexity of their projection on their Seifertsurface.
 A locally hyperbolic 3manifold that is not homotopy equivalent to any
hyperbolic 3manifold, Conform. Geom. Dyn. 24 (2020), 118130. In this paper we improve the example in our first paper by showing that there exists a locally hyperbolic 3manifolds with no locally divisible subgroups that is not homotopy equivalent to any hyperbolic 3manifold.  Hyperbolic limits of Cantor set complements in the sphere with Franco Vargas Pallete; Bulletin of the London Mathematical Society, vol. 54, issue 3, pages 11041119, 2022. In this paper we show that hyperbolic Cantor set complements in the 3sphere are dense, with respect to the geometric topology, in the set of hyperbolic manifolds without rank two cusps that admit embeddings in the 3sphere.
 On volumes and filling collections of multicurves with José Andrés Rodríguez Migueles and Andrew Yarmola; Journal of Topology, 15(3):1107–1153, 2022. In this paper we study links in the projective bundle of surfaces that arise as canonical lifts of filling collections of simple closed curves. For large classes of these links we give volumes asymptotics that involve combinatorial data coming the curves.
 Effective contraction of skinning maps, joint work with Lorenzo Dello Schiavo, accepted at Proceedings of the AMS, 2022. In this work we give explicit bounds on the contraction factor of the skinning map over the moduli space of hyperbolic surfaces.
 Volume bounds for the canonical lift complement of a random geodesic, joint work Yannick Krifka, Didac MartinezGranado , Franco Vargas Pallete; accepted at Transactions of the AMS. In this paper we study random geodesic obtained by flowing in random directions under the geodesic flow and their canonical lifts in the projective tangent bundle. For this random model we give a probabilistic estimate of the volume of the corresponding lift complement that is sublinear with respect to the length of the geodesic.
PrePrints:

 Hyperbolization of infinite type 3manifolds; April 2019 preprint, submitted. In this paper we give the first known hyperbolisation results for a large class of infinitetype hyperbolic 3manifolds.
Collaborators: