Mirror stabilizers for lattice
complex hyperbolic triangle groups
.
Published Online in Geom. Dedicata,
available on arXiv.
On subgroups of finite index in complex hyperbolic lattice triangle groups
.
to appear in Exp. Math. (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 1cusped neat ball quotient).
Relevant computer code can be found here on gitlab.
Torsion in 1cusped
Picard modular groups.
(with M. Xu)
to appear in Transform. Groups. (arXiv)
Relevant computer code can be found here on gitlab.
On the geometry of a Picard modular
group.
Groups Geom. Dyn. 17 (2023) 13931416 (Published version, arXiv)
New
nonarithmetic complex hyperbolic lattices II.
(with
J. R. Parker and
J. Paupert)
Michigan Math J. 70 (2021)
133205. 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.
A new nonarithmetic
lattice in PU(3,1).
Algebr. Geom. Topol. 20 (2020) 925963. Published version.
Volumes of 3ball
quotients as intersection numbers.
Trans. Amer. Math. Soc. 373 (2020) 343383.
Published version.

Nonarithmetic
lattices and the Klein quartic.
J. Reine Angew. Math. 754 (2019) 253279.
Published Version.

Nonarithmetic
ball quotients from a configuration of elliptic curves in an Abelian
surface.
Comment. Math. Helv. 93 (2018) 533554.
Published
Version.

A
1parameter family of spherical CR uniformizations of the figure
eight knot complement.
Geom. Topol. 20 (2016), 35713621. Published version.

New
nonarithmetic complex hyperbolic lattices.
(with
J. R. Parker and
J. Paupert)
Invent. Math. 203 (2016), 681771.
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.

On spherical CR uniformization of
3manifolds.
Exp. Math. 24 (2015)
355370, Published
version.

Complex hyperbolic geometry of the figure
eight knot
(with
E. Falbel)
Geom. Topol. 19 (2015)
237293. Published
version.

Census of the complex hyperbolic sporadic triangle groups.
(with J. R. Parker and J. Paupert)
Exp. Math. 20 (2011) 467486. Published version.
The relevant computer program can be found here.

Almost quarterpinched Kähler metrics and Chern numbers.
(with H. Seshadri)
Proc. Amer. Math. Soc. 139 (2011) 25712576.
Published
version.

Forgetful maps between DeligneMostow ball quotients.
Geom. Dedicata 150 (2011) 377389. Published
version.
In order to see the source code of the related computer program,
download Tauto.jar.

Deforming the RFuchsian (4,4,4)triangle group into a lattice.
Topology 45 no.6 (2006) 9891020.
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).

Dirichlet domains for the Mostow lattices.
Experiment. Math. 14 (2005) 467490.
Published version.
See the relevant Java applet

New constructions of fundamental polyhedra in complex hyperbolic space.
(with
E. Falbel and
J.Paupert)
Acta Math. 194 (2005) 155201. Published version.

A negatively curved Kähler threefold not covered by the ball.
Invent. Math. 160 (2005) no.3, 501525. Published version.

On the universal cover of certain exotic Kähler surfaces of negative curvature.
Math. Ann. 329 (2004) no.4, 653683. Published version.