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Recherche/research

   All my (recent) publications/preprints are available on arXiv.

Prépublications/Preprints

1. One-cusped complex hyperbolic 2-manifolds.
       (with Matthew Stover) Sep. 2024
         also available on arXiv.
   

Publications

1. Torsion in 1-cusped Picard modular groups.
       (with M. Xu)
        to appear in Transform. Groups. (arXiv)
               Relevant computer code can be found here on gitlab.
   

2. Mirror stabilizers for lattice complex hyperbolic triangle groups .
         Geom. Dedicata 218 (2024) Published Online, available on arXiv.
   

3. On subgroups of finite index in complex hyperbolic lattice triangle groups .
        Exp. Math. 33 (2024) 456-481 (published online or arXiv)
               The above link points to a version of the paper later than publication, where some typos were corrected (including the Magma command to obtain the 1-cusped neat ball quotient).
               Relevant computer code can be found here on gitlab.
   

4.    On the geometry of a Picard modular group.
         Groups Geom. Dyn. 17 (2023) 1393-1416 (Published version, arXiv)
   

5.    New non-arithmetic complex hyperbolic lattices II.
       (with J. R. Parker and J. Paupert)
         Michigan Math J. 70 (2021) 133-205. Published version.
               Software that performs the computations needed in the paper can be found here.
               Pictures of some of these fundamental domains can be found here or there.

6.    A new non-arithmetic lattice in PU(3,1).
          Algebr. Geom. Topol. 20 (2020) 925-963. Published version.
   

7.    Volumes of 3-ball quotients as intersection numbers.
         Trans. Amer. Math. Soc. 373 (2020) 343-383. Published version.
   

8.    Non-arithmetic lattices and the Klein quartic.
         J. Reine Angew. Math. 754 (2019) 253-279. Published Version.
   

9.    Non-arithmetic ball quotients from a configuration of elliptic curves in an Abelian surface.
         Comment. Math. Helv. 93 (2018) 533-554. Published Version.
   

10.    A 1-parameter family of spherical CR uniformizations of the figure eight knot complement.
          Geom. Topol. 20 (2016), 3571-3621. Published version.
    

11.    New non-arithmetic complex hyperbolic lattices.
        (with J. R. Parker and J. Paupert)
          Invent. Math. 203 (2016), 681-771. Published version.
                Software that performs the computations needed in the paper can be found here.
                Pictures of these (and some more) fundamental domains can be found here or there.

12.     On spherical CR uniformization of 3-manifolds.
          Exp. Math. 24 (2015) 355-370, Published version.

13.     Complex hyperbolic geometry of the figure eight knot
        (with E. Falbel)
          Geom. Topol. 19 (2015) 237-293. Published version.

14.     Census of the complex hyperbolic sporadic triangle groups.
        (with J. R. Parker and J. Paupert) 
          Exp. Math. 20 (2011) 467-486. Published version.
                The relevant computer program can be found here.

15.     Almost quarter-pinched Kähler metrics and Chern numbers.
        (with H. Seshadri)
           Proc. Amer. Math. Soc. 139 (2011) 2571-2576. Published version.

16.     Forgetful maps between Deligne-Mostow ball quotients.
          Geom. Dedicata 150 (2011) 377-389. Published version.
               In order to see the source code of the related computer program, download Tauto.jar.

17.     Deforming the R-Fuchsian (4,4,4)-triangle group into a lattice.
           Topology 45 no.6 (2006) 989-1020. Published version.
               The relevant applet can be found here.
               Prettier pictures than the ones in the published paper can be seen here (these were obtained with a more recent version of my computer program).

18.     Dirichlet domains for the Mostow lattices.
           Experiment. Math. 14 (2005) 467-490. Published version.
               See the relevant Java applet

19.     New constructions of fundamental polyhedra in complex hyperbolic space.
        (with E. Falbel and J.Paupert)
           Acta Math. 194 (2005) 155-201. Published version.

20.     A negatively curved Kähler threefold not covered by the ball.
           Invent. Math. 160 (2005) no.3, 501-525. Published version.

21.     On the universal cover of certain exotic Kähler surfaces of negative curvature.
           Math. Ann. 329 (2004) no.4, 653-683. Published version.

Thèses/Theses

•    Géométrie Complexe et Courbure Négative
         Mémoire d'Habilitation à Diriger des Recherches (soutenu le 29 octobre 2010 à l'Institut Fourier).

•    Complex surfaces of negative curvature
         Ph.D. thesis, University of Utah, 2001 (under the supervision of Domingo Toledo).

Groupe de travail SGT (Automne 2014)

Structures géométriques sur les variétés de dimension trois.

Dernière mise à jour: Sep 13, 2024