Laboratoire de Mathématiques
U.F.R. Sciences Exactes et Naturelles
Moulin de la Housse - BP 1039
51687 REIMS cedex 2
France
Office: +33 (0)3 26 91 83 93
e-mail: firstname.lastname(at)univ-reims.fr
I am a graduate of Moscow School for Mathematics No 2 (web site in Russian), class of 1981
PhD received in 1989 from Moscow State University
Research |
Areas of interest:
-projective differential geometry (Schwarzian derivative,...);
-discrete integrable systems (Pentagram map,...);
-algebraic combinatorics (Coxeter friezes, square identities,...);
-cohomology of Lie algebras of vector fields and diffeomorphism groups (Virasoro algebra, modules of differential operators on smooth manifolds,...);
-graded commutative algebras (quaternions, octonions, Lie antialgebras,...).
Together with Christian Duval and Pierre Lecomte we developed equivariant quantization.
See my publications at Google scholar:
Google scholar,
I am on the Editorial Board of:
Journal of Nonlinear Mathematical Physics,
The Book |
You can download (a preprint version of) my book with Sergei Tabachnikov:
Cambridge University Press, Cambridge Tracts in Mathematics, 165, 2005.
Talks |
Listen to the talk on The Pentagram map: a discrete integrable system.
Some of my publications (by subjects) |
"Whas is" Papers:
Well, Papa, can you multiply triplets? (with S. Morier-Genoud)
What is... the Schwarzian derivative? (with S. Tabachnikov)
Hurwitz square identities & applications:
On fibrations with flat fibers. (with S. Tabachnikov)
Extremal set theory, cubic forms on ${\mathbb F}_2^n$ and Hurwitz square identities. (with S. Morier-Genoud)
Orthogonal Designs and a Cubic Binary Function. (with S. Morier-Genoud)
A series of algebras generalizing the octonions and Hurwitz-Radon identity. (with S. Morier-Genoud)
New solutions to the Hurwitz problem on square identities. (with A. Lenzhen and S. Morier-Genoud)
Graded-commutative algebra:
Higher Trace and Berezinian of Matrices over a Clifford Algebra. (with T. Covolo,N. Poncin)
Simple graded commutative algebras. (with S. Morier-Genoud)
Alternated Hochschild Cohomology. (with P. Lecomte)
Supertransvectants and symplectic geometry. (with H. Gargoubi)
Pentagram map, discrete integrable systems, combinatorics:
Liouville-Arnold integrability of the pentagram map on closed polygons. (with R. Schwartz, S. Tabachnikov)
The Pentagram map: a discrete integrable system. (with R. Schwartz, S. Tabachnikov)
Linear difference equations, frieze patterns and combinatorial Gale transform. (with S. Morier-Genoud, R. Schwartz and S. Tabachnikov)
2-frieze patterns and the cluster structure of the space of polygons. (with S. Morier-Genoud and S. Tabachnikov)
Introducing supersymmetric frieze patterns and linear difference operators. (with S. Morier-Genoud and S. Tabachnikov)
$\SL_2(\Z)$-tiling of the torus, Coxeter-Conway friezes and Farey triangulations. (with S. Morier-Genoud and S. Tabachnikov)
Coxeter's frieze patterns and discretization of the Virasoro orbits. (with S. Tabachnikov)
Quasiperiodic motion for the Pentagram map (with R. Schwartz, S. Tabachnikov)
Equivariant quantization and symbol calculus:
Projectively Equivariant Symbol Calculus. (with P. Lecomte)
Conformally equivariant quantization: existence and uniqueness. (with C. Duval and P. Lecomte)
Projectively Equivariant Quantization and Symbol Calculus: Noncommutative Hypergeometric Functions. (with C. Duval)
Conformally equivariant quantum Hamiltonians. (with C. Duval)
Differential operators on supercircle: conformally equivariant quantization and symbol calculus. (with H. Gargoubi and N. Mellouli)
Projectively and Conformally Invariant Star-Products. (with C. Duval and A. El Gradechi)
Modules of of differential operators:
Riemannian curl in contact geometry. (with S. Bouarroudj)
Linear differential operators on contact manifolds. (with C. Conley)
Space of Second-Order Linear Differential Operators as a Module over the Lie Algebra of Vector Fields. (with C. Duval)
Cohomology of the Vector Fields Lie Algebra and Modules of Differential Operators on a Smooth Manifold. (with P. Lecomte)
Multi-Parameter Deformations of the Module of Symbols of Differential Operators. (with B. Agrebaoui, F. Ammar, P. Lecomte)
Modules of Differential Operators on the Real Line. (with H. Gargoubi)
Space of Linear Differential Operators on the Real Line as a Module over the Lie Algebra of Vector Fields. (with H. Gargoubi)
Three Cocycles on Diff(S1) Generalizing the Schwarzian Derivative. (with S. Bouarroudj)
Symmetries of Modules of Differential Operators. (with H. Gargoubi and P. Mathonet)
Generalized transvectants-Rankin-Cohen brackets. (with P. Redou)
Virasoro, KdV and generalizations:
Looped Cotangent Virasoro Algebra and Non-Linear Integrable Systems in Dimension 2 + 1. (with C. Roger)
Generalizations of Virasoro group and Virasoro algebra through extensions by modules of tensor-densities on $S^1$. (with C. Roger)
Extension of the Virasoro and Neveu–Schwarz Algebras and Generalized Sturm–Liouville Operators. (with P. Marcel and C. Roger)
The super Korteweg-de Vries equation as an Euler equation. (with B. Khesin)
Symplectic leaves of the Gel'fand-Dikii bracket and homotopy classes of nondegenerated curves. (with B. Khesin)
Deformations of Poisson brackets and extensions of Lie algebras of contact vector fields. (with C. Roger)
Deforming the Lie Algebra of Vector Fields on $S^1$ Inside the Poisson Algebra on $T^∗ S^1$. (with C. Roger)
Deforming the Lie algebra of vector fields on $S^1$ inside the Lie algebra of pseudodifferential symbols on $S^1$. (with C. Roger)
On identities in the Lie algebra of vector fields on the real line. (an old paper in Russian of A.A. Kirillov + a paper in English with A.A. Kirillov and O. Udalova)
Projective Differential Geometry:
Schwarzian derivative related to modules of differential operators on a locally projective manifold.(with S. Bouarroudj)
Sturm theory, Ghys theorem on zeroes of the Schwarzian derivative and flattening of Legendrian curves. (with S. Tabachnikov)
Lorentzian Worldlines and the Schwarzian Derivative. (with C. Duval)
Theorem on six vertices of a plane curve via Sturm theory. (with L. Guieu and E. Mourre)
Projective geometry of polygons and discrete 4-vertex and 6-vertex theorems. (with S. Tabachnikov)
Classification of contact-projective structures on supercircles. (with Yu. Chekanov and O. Ovsienko)
Hyperbolic Caratheodory conjecture.(with S. Tabachnikov)
My students |
Hichem Gargoubi (PhD 1997)
Patrick Marcel (PhD 1999)
Sofiane
Bouarroudj (PhD 1999)
Sabin Loubon-Djounga (PhD 2001)
Pascal
Redou (PhD 2002)
Yael Fregier (PhD 2005)
Najla Mellouli (PhD 2010)
Tiffany Covolo (PhD 2014)
Marie Kreusch (PhD 2015)