Research
My research interests lie in low-dimensional geometry and topology. More precisely, I study hyperbolic geometry (mostly complex), reflection groups, and lattices in rank 1 semisimple Lie groups.
My research is currently supported by NSF grant DMS 1007340.
Publications:
- (with E. Falbel) Fundamental domains for finite subgroups in U(2) and configurations of Lagrangians. Geom. Dedicata 109 (2004), 221-238. pdf, ps.
- (with M. Deraux and E. Falbel) New constructions of fundamental polyhedra in complex hyperbolic space. Acta Math. 194 (2005), 155-201. pdf, ps.
- Elliptic triangle groups
in PU(2,1), Lagrangian triples and momentum
maps. Topology 46 (2007), 155-183. Preprint (pdf).
- Applications moment, polygones de configuration et groupes discrets de réflexions complexes dans PU(2,1). Séminaire de théorie spectrale et géométrie, Grenoble. TSG 24 (2007), 45-60. Preprint (pdf).
- (with J. Parker) Unfaithful
complex hyperbolic triangle groups II: Higher order
reflections. Pacific J. Maths. 239 (2009), 357-389. Preprint (pdf).
- Unfaithful
complex hyperbolic triangle groups III: arithmeticity and commensurability . Pacific J. Maths. 245 (2010), 359-372. Preprint (pdf).
- (with M. Deraux and J. Parker) Census of the complex hyperbolic sporadic triangle groups. To appear in Experiment. Math. Preprint (pdf).
- Non-discrete hybrids in SU(2,1). To appear in Geom. Dedicata. Preprint (pdf).
Preprints and work in progress:
- (with M. Deraux and J. Parker) A family of new non-arithmetic complex hyperbolic lattices. In preparation.
- (with P. Will) Real reflection triangle groups in PU(n,1): decomposable pairs and traces. In preparation.
PhD thesis:
- Configurations of Lagrangians, fundamental domains and discrete subgroups of PU(2,1), Ph.D. Thesis, Université Paris 6, 2005 (advisor: Elisha Falbel) :
pdf (3 MB), ps (9.9 MB), compressed ps file ps.gz (2.1 MB).
- Thesis abstract : pdf.
Research statement:
In english (october 2009), pdf.
Research project:
Version française (mars 2009), pdf.
English version (september 2009), pdf.
Curriculum Vitae:
- Version française, pdf.
- English version, pdf.