Research activities
My research work lies at the interface between algebraic geometry and number theory and often consists in addressing a pure mathematical problem coming from applied areas, such as cryptography and coding theory.
In my Ph.D thesis (supervised by Yves Aubry) I considered the problem of building singular curves over finite fields with many rational points. My work is based on notions and tools from commutative algebra, algebraic geometry and combinatorics.
More recently I have started working in a young and very active subfield of post-quantum cryptography, called isogeny-based cryptography, which is based on the arithmetic of elliptic curves over finite fields. In this context I am mainly interested in mathematical problems which are behind the security of isogeny-based cryptosystems, such as the study of the structure of supersingular isogeny graphs and the efficient computation of the endomorphism ring of a supersingular elliptic curve defined over a finite field.
I am also interested in problems from number theory that can be reduced to the study of algebraic varieties over finite fields.
Finally, in my reaseach work I love collaborating with people in order to exchange our different points of view on a given topic. To me, this is the best way to learn new tools and methods, while discovering and having fun!
Publications
Here is the list of my publications:
In preparation:
- Improved algorithms for computing endomorphism rings, with Jenny Fuselier, Mark Kozek, Travis Morrison et Changningphaabi Namoijam.
Ph.D thesis
Nombre de points rationnels des courbes singulières sur les corps finis
Language: French (sorry!)
Supervisor: Yves Aubry
Defended on July 6, 2016, at Aix-Marseille Université, in Marseille
Master thesis
Domini Almost Dedekind
Language: Italian (sorry again!)
Supervisor: Stefania Gabelli
Defended on July 18 2012 at Università degli Studi di Roma 3, in Rome