Elisha Falbel

email : elisha.falbel at imj-prg.fr
Bureau: 1626-520, Jussieu, 75005 Paris
Téléphone: 01 44 27 53 46
URL: http://webusers.imj-prg.fr/~elisha.falbel/

Travaux récents :

Character varieties for SL(3,C): the figure eight knot. Avec A. Guilloux, P.-V. Koseleff, F. Rouillier, M. Thistlethwaite. (arxiv ) 2014.

Duality and invariants of representations of fundamental groups of 3-manifolds into PGL(3,C). Avec Q. Wang. (arxiv ) 2014.

A flag structure on a cusped hyperbolic 3-manifold. Avec R. S. Thebaldi. ( Hal). To appear in Pacific J. Math.

Diffeomorphisms preserving R-circles in three dimensional CR manifolds. Avec J. M. Veloso. ( pdf). 2013. To appear in Math. Nachr.

Representations of fundamental groups of 3-manifolds into PGL(3;C): Exact computations in low complexity. Avec P.-V. Koseleff et F. Rouillier. ( pdf). 2013. To appear in Geom. Dedicata.

Branched spherical CR structures on the complement of the figure eight knot. Avec Jieyan Wang. ( pdf). 2013. Michigan Math. J. 63 (2014), no. 3, 635-667.

Complex hyperbolic geometry of the figure eight knot. Avec Martin Deraux. ( pdf). Geom. Topol. 19 (2015), no. 1, 237-293.

Local rigidity for SL(3,C) representations of 3-manifolds groups. Avec N. Bergeron, A. Guilloux, P.-V. Koseleff et F. Rouillier. ( pdf) 2012. Exp. Math. 22 (2013), no. 4, 410-420.

Tetrahedra of flags, volume and homology of SL(3). Avec N. Bergeron et A. Guilloux. ( pdf). 2011. Geom. Topol. 18 (2014), no. 4, 1911-1971.

A combinatorial invariant for Spherical CR structures. Avec Qingxue Wang. ( pdf). 2010. Asian J. Math. 17 (2013), no. 3, 391-422.

A Lorentz form associated to contact sub-conformal and CR manifolds. Avec J. M. Veloso. Kodai Math. J. 37 (2014), no. 2, 405-426.

Travaux moins récents :

Generators of a Picard modular group in two complex dimensions. Avec Gábor Francsics, Peter D. Lax et John Parker.
Proc. Amer. Math. Soc. 139 (2011), no. 7, 2439-2447

The geometry of the Gauss-Picard modular group. Avec Gábor Francsics et John Parker.
Math. Ann. 349 (2011), no. 2, 459-508.

A Volume function for Spherical CR tetrahedra.
Quarterly Journal of Math. 62 (2011), no. 2, 397 - 415. ( ps)

The PU(2,1) configuration space of four points in S3 and the Cross-Ratio Variety. Avec Ioannis Platis.
Math. Annalen. 340 (2008), no. 4, 935-962. ( ps)

Compacité à la Mahler-Mumford pour les groupes fuchsiens dans un espace symétrique de rang un. Avec Richard Wentworth. ( pdf).
New version: On Products of Isometries of Hyperbolic Space.
Topology Appl. 156 (2009), no. 13, 2257-2263.( pdf).

Geometric structures associated to triangulations as fixed point sets of involutions.
Topology and its Applications 154 (2007), no. 6, 1041-1052. ( pdf). New version with some corrections ( ps).

A spherical CR structure on the complement of the figure eight knot with discrete holonomy. Yet another version.
Journal of Differential Geometry. 79 (2008), no. 1, 69-110. ( ps)

Unitary Representations and triples of Lagrangians. Avec Richard Wentworth.
Topology 45 (2006), no. 1, 65-99. ( ps)

A bilinear form associated to contact sub-conformal and CR-manifolds. Avec Jose Miguel Veloso.
Journal of Differential Geometry and its Applications. ( ps)

The geometry of Eisenstein-Picard modular group. Avec John Parker.
Duke Math. Journal 131 (2006), no. 2, 249--289. ( ps)

New constructions of fundamental polyhedra in complex hyperbolic space. Avec Martin Deraux et Julien Paupert.
Acta Mathematica 194 (2005), 155-201. ( pdf)

Fundamental domains for finite subgroups of U(2) and Configurations of Lagrangians. Avec Julien Paupert.
Geom. Dedicata 109 (2004), 221--238. ( ps)

Classifying triples of Lagrangians in a Hermitian vector space. Avec J.-P. Marco, F. Schaffhauser.
Topology Appl. 144 (2004), no. 1-3, 1--27. ( pdf)

Measures of Transverse Paths in Sub-Riemannian Geometry. Avec F. Jean.
J. Anal. Math. 91 (2003), 231--246. ( ps)

The moduli space of the modular group in complex hyperbolic geometry. Avec J. Parker.
Inventiones Mathematicae. 152 (2003), no. 1, 57--88. (ps)

A simple proof of the Riemann Mapping Theorem for Domains with Spherical Boundary.
Complex Var. Theory Appl. 48 (2003), no. 3, 277--282.( ps)

A circle of Modular groups in PU(2,1). Avec P.-V. Koseleff.
Math. Res. Lett. 9 (2002), no. 2-3, 379--39 ( ps)

Rigidity and flexibility of triangle groups in complex hyperbolic geometry. Avec P.-V. Koseleff.
Topology 41 (2002), no. 4, 767--786 ( ps)

Finite groups generated by involutions on Lagrangian planes of C^2.
Canad. Math. Bull. 44 (2001), no. 4, 408--419 ( ps)

Travaux du siècle dernier :
(avec V. Zocca), A Poincaré's polyhedron theorem for complex hyperbolic geometry, J. Reine Angew. Math. 516 133--158 (1999).
(avec P. Bieliavsky et C. Gorodski), The classification of contact sub-Riemannian symmetric spaces. Pacific Journal of Mathematics 188 65-82 (1999).
(avec J. M. Veloso), A Parallelism for conformal sub-Riemannian Geometry. Forum mathematicum 10, no. 4, 453-478 (1998).
(avec C. Gorodski, M. Rumin), On the holonomy of sub-Riemannian spaces. International Journal of Mathematics 8, No. 3, 317-344 (1997).
(avec C. Gorodski), On homogeneous sub-Riemannian manifolds of dimensions 3 and 4. Geometriae Dedicata 62, 227-252 (1996).
(avec C. Gorodski), On contact symmetric sub-Riemannian spaces. Annales Scient. Ecole Norm. Sup. 4, 28, 571-589 (1995).
(avec C. Gorodski, J. M. Veloso). Conformal sub-Riemannian geometry in dimension 3. Matemática Contemporanea 9, 61-73 (1995).
(avec N. Gusevskii), Spherical CR-manifolds of dimension three. Bulletin of Braz. Math. Soc. 25, 1, 31-56 (1994).
(avec J. M. Veloso, J. A. Verderesi). Constant curvature models in sub-Riemannian geometry. Matemática Contemporanea 4, 119-125 (1993).
Non-embeddable CR-manifolds and Surface singularities. Inventiones Mathematicae, 108, 49-65 (1992).
Topological obstructions to the embeddability of CR-manifolds. Matemática Contemporanea 1, 45-55 (1991).

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Enseignement

Probabilité Polytech : polycopié par Claire Le Goff pdf
LM110 (Analyse 1 - Fonctions). Feuilles d'exercices 2011-2012 (pdf).
LM256 (Analyse vectorielle, intégrales multiples). Corrigé de l'examen 2008-2009 (pdf).
LM301. Corrigé de l'examen 2008 (pdf).
LM200. Corrigé de l'examen 2008 (pdf).
Introduction a la géométrie hyperbolique (pdf).

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l'Ecole Doctorale de Sciences Mathématiques de Paris