University of French Polynesia
BP 6570, 98702 FAA'A Tahiti
Phone: +689 87 32 07 87
Currenly I am PhD student in mathematics. Heve is my CV in english.
- Algebraic geometry over finite fields (the number of rational points and its distribution, zeta-function, the lower Weil-Serre bound, varieties having no points of given degrees, hyperelliptic curves)
- Polynomials over finite fields (the value set, families of polynomials having specific values, explicit constructions)
Bounds on the genera of smooth curves over finite fields having a prescribed number of rational points.
In particular, in the case of hyperelliptic curves and cyclic coverings of the projective line.
Preprints and drafts
- On the linear bounds on the genera of pointless hyperelliptic curves (arxiv)
- On the explicit bound on the genera of curves with given number of points (draft, will appear soon)
- June 2017, Arithmetic, Geometry, Cryptography and Coding Theory, Marseilles, France.
Talk: On the linear bounds on the genus of pointless curves
- June 2015, Fifth School-Conference on Lie Algebras, Algebraic Groups and Invariant Theory, Samara, Russia.
Talk: Hyperelliptic curves over finite fields having no rational points
September 2017, Brocante Mathématique, IRMAR, Université de Rennes 1, Rennes, France.
Talk: How to solve a Rubik's Cube of size 100?
Abstract. A Rubik's Cube... This puzzle provides a great challenge for people all over the World. Also, the search of solutions of the puzzle (in the case of arbitrary size) is a curious research problem. In this 5-minutes talk a new approach to the problem is presented. Namely, we introduce a simple type of transformations of Rubic's Cubes that aims to solve the puzzle algorithmically (even without involving computer computations). It appears that the structure of the group generated by all transformations of the type can be written down explicitly (it is the product of some alternative groups). If time permits, we will make an interactive demonstration.
25 September 2019, Rennes, France