Papers and such

Preprints, Papers accepted for publication, Published papers, Retracted paper(s),  or Older stuff I never submitted

Preprints

• • Holomorphic maps between moduli spaces II, with Rodrigo de Pool, preprint 2024.

  • On the distribution of the components of a multicurve of given type, with Viveka Erlandsson, preprint 2024

  • Effective Estimation of the Dimension of a Manifold from Random Samples, with Lucien Grillet, preprint 2022.

  • Deciding when two curves are of the same type, with Thi Hanh Vo, preprint 2020.

  • Mirzakhani's Curve Counting: from simple to all, with Viveka Erlandsson, preprint 2022 (revised version of a note from 2019).

Program

I dn't know how to program, but I have been wasting some amount of time making my computer sweat calculating things about the punctured torus. If you are bored you can go here to get the program (in Python). Here you have a compiled version that runs on Windows.  I am sure that, besides being a patent waste of time, there all sorts of problems with the program. Still, please let me know.

Published papers

• Thick hyperbolic 3-manifolds with bounded rank, with I. Biringer, accepted for publication in Memoirs of the AMS.

• Counting geodesics of given commutator length, with Viveca Erlandsson, accepted for publication in Forum of Mathematics, Sigma 11, 2023.

• Harmonic extensions of quasiregular maps, with P. Pankka, accepted for publication in the Journal of Differential Geometry.

• Counting and equidistribution of reciprocal geodesics and dihedral groups, with Viveka Erlandsson, IMRN 13, 2024.

• Mapping class group orbit closures for non-orientable surfaces, with Viveka Erlandsson, Matthieu Gendulphe and Irene Pasquinelli, GAFA 33, 2023.

• Counting curves on orbifolds, with Viveka Erlandsson, Transactions of the LMS 9, 2022.

• Bubbling of quasiregular maps, with Pekka Pankka, Math. Annalen 2022.

• Distribution in the unit tangent bundle of the geodesics of given type, with Viveka Erlandsson, Ergodic Theory and Dynamical Systems  2022.

• Weil-Petersson translation length and manifolds with many fibered fillings, with Chris Leininger, Yair Minsky and Sam Taylor, Advances in Mathematics 376, (2021).

• Genericity of pseudo-Anosov mapping classes, when seen as mapping classes, with Viveka Erlandsson and Jing Tao, Enseign. Math. 66 (2020).

• Surface groups in the group of germs of analytic diffeomorphisms in one variable, with Serge Cantat, Dominique Cerveau, and Vincent Guirardel, Enseign. Math. 66 (2020). 

• Counting curves and the stable length of currents, with V. Erlandsson and H. Parlier, Journal of the European Math. Soc. 22, 2020.

• Ranks of mapping tori via the curve complex, with I. Biringer, Journal für die reine und angewandte Mathematik (Crelle) 748, 2019.

• Free Vs. Locally Free Kleinian Groups, with P. Pankka, Journal für die reine und angewandte Mathematik (Crelle) 746, 2019.

• A remark about critical sets in R^3, Revista Mat. Iberoamericana 25, 2019.

• Geodesic currents and counting problems, with K. Rafi, GAFA 29, 2019.

• Counting curve types, with T. Aougab, accepted for publication in the American Journal of Mathematics 140, 2018.

• Discrete groups without finite quotients, with T. Cremaschi, Topology and its Application 248, 2018.

• Surface groups of diffeomorphisms of the interval, with L. Marquis, Israel Journal of Math 227, 2018.

• Variations on a Theorem of Birman and Series, with A. Lenzhen, Annales de l'Institut Fourier 68, 2018.

• Holomorphic maps between moduli spaces, with S. Antonakoudis and J. Aramayona, Annales de l'Institut Fourier 68, 2018.

• Dimension invariants of outer automorphism groups, with D. Degrijse, Groups, Geometry and Dynamics 11, 2017.

• Geometric filling curves on surfaces, with A. Basmajian and H. Parlier, Bulletin of the London Mathematical Society 49, 2017.

• Geometric dimension of lattices in classical simple Lie groups, with J. Aramayona, D. Degrijse and C. Martinez-Perez, Journal of Topology  10, 2017.

• Recurrence of multiended planar triangulations, with A. Nachmias and O. Gurel-Gurevich, Electronic Communications in Probability 22, 2017.

• Counting Curves in Hyperbolic Surfaces, with V. Erlandsson, GAFA 26, 2016.

• Rigidity phenomena in mapping class groups, with J. Aramayona, Handbook of Theichmüller theory, Vol. VI, 2016.

• Bounded combinatorics and uniform models for hyperbolic 3-manifolds, with J. Brock, Y. Minsky and H. Namazi, Journal of Topology 9, 2016.

• Three techniques for obtaining algebraic circle packings, with L. Louder and A. Mishenko, Michigan Math. Journal 63, 2014.

• Distributional limits of Riemannian manifolds and graphs with sublinear genus growth, with H. Namazi and P. Pankka, GAFA 24, 2014.

• A remark on homomorphisms from right-angled Artin groups to mapping class groups, with J. Aramayona, C. R. Acad. Sci. Paris 351, 2013.

• Shearing coordinates and convexity of length functions with M. Bestvina, K. Bromberg, K. Fujiwara, American Journal of Math 135, 2013.

• Periodic maximal flats are not peripheral, with A. Pettet, Journal of Topology, 2013.

• Commuting tuples in reductive groups and their maximal compact subgroups, with A. Pettet, Geometry and Topology 17, 2013.

• Some groups of mapping classes not realized by diffeomorphisms with M. Bestvina and T. Church, Comment. Math. Helv. 88, 2013.

• A Cantor set with hyperbolic complement, with M. Stower, Conformal Geometry and Dynamics 17, 2013.

• Homomorphisms between mapping class groups, with J. Aramayona, Geometry and Topology 16, 2012.

• Non-realizability, ending laminations and the density conjecture, with H. Namazi, Acta Math 209, 2012.

• Genericity of Pseudo-Anosovs in the Torelli group, with J. Malestein, IMRN, 2012.

• Geometric limits of knot complements, II: Graphs determined by their complements with A. Kent, Mathematische Zeitschrift 271, 2012.

• On the fundamental group of Hom(Z^k,G), with J. M. Gomez and A. Pettet, Mathematische Zeitschrift 271, 2012.

• A finiteness theorem for hyperbolic 3-manifolds, with I. Biringer, Journal of the LMS 84, 2011.

• Automorphisms of the graphs of free splittings, with J. Aramayona, Michigan Math Journal 60, 2011.

• Exotic quasi-conformally homogeneous surfaces, with P. Bonfert-Taylor, R. Canary and E. Taylor, Bull. LMS. 2011.

• Algebraic and geometric convergence of representations into PSL_2C, with I. Biringer, Geometry and Topology 14, 2010.

• A remark on the action of the mapping class group on the unit tangent bundle, Annales de la Faculte des Sciences de Toulouse, Vol. XIX, 2010.

• Geometric limits of knot complements, with J. Purcell, Journal of Topology 2010.

• Finitely generated subgroups of lattices in PSL(2,C), with Y. Glasner and P. Storm, Proceedings of the American Mathematical Society 138, 2010.

• Chords, light and another characterization of the round sphere, with B. Schmidt, Commentarii Mathematici Helvetici 85, 2010.

• Injections of mapping class groups with J. Aramayona and C. Leininger, Geometry & Topology 13, 2009.

• Heegaard splittings and pseudo-Anosov maps, with H. Namazi, GAFA 19, 2009.

• The rank of the fundamental group of certain hyperbolic 3-manifolds fibering over the circle, in The Zieschang Gedenkschrift, Geometry and Topology Monographs, Vol. 14, 2008.

• Minimality of the well-rounded retract, with A. Pettet, Geometry and Topology 12, 2008.

• The spine which was no spine, with A. Pettet, L'Enseignement Mathematique 54, 2008.

• Two applications of the natural map, Geometriae Dedicata 133, 2008

• Geometry, Heegaard splittings and rank of the fundamental group of hyperbolic 3-manifolds, Geometry and Topology Monographs, Vol 12, 2007.

• Dense embeddings of surface groups, with E. Breuillard, T. Gelander and P. Storm, Geometry & Topology 10, 2006.

• Dynamics of the mapping class group action on the variety of SL_2C characters, with P. Storm, Geometry and Topology 10, 2006.

• Algebraic limits of geometrically finite manifolds are tame, with J. Brock, GAFA 16 vol. 1, 2006.

• Volume rigidity for finite volume manifolds, with J. Boland, C. Connell, Amer. J. Math. 127, 2005.

• A note on the tameness of hyperbolic manifolds, Topology 44, 2005.

• Ending laminations in the Masur domain, with G. Kleineidam, `Kleinian Groups and Hyperbolic 3-Manifolds,' Proceddings of Warwick Conference 2001, London Math. Soc., 2003.

• Boundaries of deformation spaces and Ahlfors' measure conjecture, with J. Brock, K. Bromberg and R. Evans, Publ. I.H.E.S. 98, 2003.

• Cone-manifolds with large cone-angles, Geometry and Topology, Vol. 7, 2003.

• Algebraic Convergence of Function Groups, with G. Kleineidam, Comment. Math. Helv. 77, 2002.

Never submitted or not to be submited again

These papers were either never submitted, or if they were submitted then either I never got a report or they were rejected by the journal. They land in this section because either I cannot be bothered to do anything about them, or because I was upset, or because I am just silly, or... As far as I know there are no mathematical mistakes in them and in any case remarks are welcome.

• The Heegaard genus and distances in the curve complex, preprint 2003.

• Short geodesics in hyperbolic compression bodies are not knotted, 2008 version of a 2004 preprint.

• A remark on the homotopy equivalence between SU_n and SL_nC, preprint 2010. (This is the paper where the referee decided to complain about my citing discipline asking me to point out which sections of a TWO PAGE paper I was using.)

• Diameter and spectral gap for planar graphs, with L. Louder, preprint 2012.

• Cyclic hyperbolic Veech groups in finite area, with A. Lenzhen, preprint 2017. 

• Minimal volume and Minimal entropy, part of my Ph.D.-thesis 2001.

Retracted (como decia mi abuelo Paco, un expediente sin suspensos es como un jardin sin flores)

• On the non-existence of certain branched covers, with P. Pankka, Geometry and Topology 16, 2012. Retracted in 2019. Here is the retraction letter.