My picture


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:

Projective Differential Geometry Old and New: From the Schwarzian Derivative to the Cohomology of Diffeomorphism Groups

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:

Hurwitz square identities & applications:

Graded-commutative algebra:

Pentagram map, discrete integrable systems, combinatorics:

Equivariant quantization and symbol calculus:

Modules of of differential operators:

Virasoro, KdV and generalizations:

Projective Differential Geometry:


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)