Research activities


My research topics are at the intersection of algebraic geometry, number theory and their applications to cryptography and coding theory.

In my Ph.D thesis (defended on July 6, 2016) I focused on some questions about the maximum number of rational points on a singular curve defined over a finite field.

I am also a member of the research project ANR manta: Algebraic Geometry and Coding Theory. Within this context, I am interested in codes built over higher dimensional varieties.


Publications

Here is the list of my publications:

  • Optimal and maximal singular curves, joint work with Yves Aubry, Contemporary Mathematics 686, pp. 31--43, 2017.
    pdf arXiv
  • On the maximum number of rational points on singular curves over finite fields, joint work with Yves Aubry, Moscow Math. Journal, Volume 15, Issue 4, October-December 2015, pp. 615--627.
    pdf arXiv

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

pdf slides defense

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

pdf slides


Talks

  • 03/05/2018: A singular trip through the world of algebraic curves over finite fields, Discrete Mathematics Seminar, Department of Mathematics & Statistics, University of South Florida.

    slides
  • 11/20/2016: Curve su campi finiti a singolarità prescritte, Seminario d'Algebra Commutativa, Dipartimento di Matematica e Fisica, Università degli Studi di Roma Tre.

  • 11/05/2015: Courbes optimales et maximales, Séminaire d’Arithmétique et Théorie de l’Information, Institut de Mathématiques de Marseille, Aix-Marseille Université.

  • 05/18/2015: Towards maximal singular curves over finite fields, Arithmetics, Geometry, Cryptography and Coding Theory 2015 (AGCT-2015), CIRM, Marseille.
    slides
  • 02/17/2015: Sur le nombre maximum de points rationnels d’une courbe singulière sur un corps fini, Séminaire Algébrique de l’Institut de Mathématiques de Toulon (IMATH), Université de Toulon.
  • 29/01/2015: Sur le nombre maximum de points rationnels d’une courbe singulière sur un corps fini, Séminaire d’Arithmétique et Théorie de l’Information, Institut de Mathématiques de Marseille, Aix-Marseille Université.
  • 06/11/2014: Singular curves over finite fields with many rational points, Yet Another Conference on Cryptography 2014 (YACC 2014), Île de Porquerolles, France.
    slides
  • 05/12/2014: Singular curves over finite fields with many rational points, Antalya Algebra Days XVI, Antalya, Turquie.
    slides
  • 05/14/2013: Courbes avec un nombre fixé de points rationnels, Séminaire Algébrique de l’Institut de Mathématiques de Toulon (IMATH), Université de Toulon