My research interests lie in Algebraic and Arithmetic Geometry as long as in Number Theory and Coding Theory. I work with algebraic curves and algebraic surfaces defined over finite fields, with applications to algebraic geometry codes. I am also interested in the study of abelian surfaces with some extra structure and of abelian varieties over finite fields. Also, I am keen to deepen the connection within coding theory and cryptography, and number theory and cryptography. Finally, I am passionate about the quest of maximal algebraic curves.
Have a look at my Research Project for more information about the problems I want to deal with in the near future. If you want to work on some of them together or on other related topics, do not hesitate to contact me!
Preprints and publications
- with Y. Aubry, F. Herbaut and M. Perret, Bounds on the minimum distance of algebraic geometry codes defined over some families of surfaces, to appear in Contemporary Mathematics of the AMS, arXiv
- with Y. Aubry, F. Herbaut and M. Perret, Algebraic geometry codes over abelian surfaces containing no absolutely irreducible curves of low genus, submitted, arXiv
Work in progress
with D. Kohel, On Galois representations and level 2 structures of abelian surfaces
with A. Giangreco, Cyclic or almost-cyclic abelian varieties
Algebraic geometry codes from surfaces defined over finite fields, Ph.D. thesis, available here
Nombre maximum de points rationnels de courbes de genre 3 sur les corps finis, available here (in french!)