Research

My ORCID iD:

Research interests

• Number Theory
• Arithmetic Geometry
• Function Field arithmetic (positive characteristic)

More specifically:

• Modular curves and their rational points, elliptic curves, modular forms, modular symbols
• Function field arithmetic: Drinfeld modules, Drinfeld modular curves, Drinfeld modular forms, modular symbols and automorphic forms for F_q(T)
• Galois representations coming from arithmetic.

Are you wondering what are Drinfeld modules useful for? The definitive answer can be found in this video from the TV series 24 (season 4, episode 11). Also available in French dubbed version.

Habilitation thesis

Contributions à l'étude des formes modulaires sur les corps de fonctions (in French), preliminary version of the manuscript. To be defended on November 22, 2024.

Publications et preprints

1. Torsion des modules de Drinfeld de rang 2 et formes modulaires de Drinfeld
   C. R. Math. Acad. Sci. Paris 347 (2009), 705-708. Preliminary version - published version


2. Sur les symboles modulaires de Manin-Teitelbaum pour F_q(T)
   C. R. Math. Acad. Sci. Paris 347 (2009), 845-848. Preliminary version - published version


3. Coefficients of Drinfeld modular forms and Hecke operators
   Journal of Number Theory 131 (2011), 1435-1460. Preliminary version - published version


4. Torsion des modules de Drinfeld de rang 2 et formes modulaires de Drinfeld
   Algebra & Number Theory 6-6 (2012), 1239-1288.
   Extended and improved version of the CRAS note with the same name. Preliminary version - published version


5. Galois representations and Galois groups over Q, with Sara Arias-de-Reyna, Valentijn Karemaker, Marusia Rebolledo, Lara Thomas and Núria Vila.
   In Women in numbers Europe. Research directions in number theory. Based on the presentations at the WINE workshop, Luminy, France, October 13-18, 2013, pages 191-205. Cham : Springer, 2015. Preliminary version - published version


6. Une base explicite de symboles modulaires sur les corps de fonctions
   J. Reine Angew. Math. 717 (2016), 101-132. Extended and substantially improved version of the CRAS note "Sur les symboles modulaires...". Preliminary version - published version


7. Large Galois images for Jacobian varieties of genus 3 curves, with Sara Arias-de-Reyna, Valentijn Karemaker, Marusia Rebolledo, Lara Thomas and Núria Vila.
   Acta Arith., 174(4) (2016), 339-366. Preliminary version - published version


8. Sturm-type bounds for modular forms over function fields, with Fu-Tsun Wei.
   Journal of Number Theory 237 (August 2022), 67-98. Preliminary version - published version


9. Drinfeld singular moduli, hyperbolas, units with Bruno Anglès, Vincent Bosser et Fabien Pazuki.
   Preprint April 2024, 41 pages. arXiv version.


10. Non-perfect pairings between Hecke algebra and modular forms over function fields.
    Preprint August 2024, 21 pages. arXiv version.


11. Ogg's conjectures over function fields with Sheng-Yang Kevin Ho and Mihran Papikian.
    Expository paper, September 2024, 40 pages. Preliminary version.

PhD dissertation

• Torsion rationnelle des modules de Drinfeld (135 pages in French).
  Doctoral thesis, University Paris 7, prepared under the supervision of Loïc Merel.

Doctoral supervision

From 2019 to 2023, I was the co-advisor of the PhD thesis of Valentin Petit with Christophe Delaunay. The thesis gave rise to two papers:
• Non-divisible point on a two-parameter family of elliptic curves. Research in Number Theory 8 (2022). Preliminary version - published version
• Explicit computation of the modular parametrization of elliptic curves over function fields by Drinfeld modular curves. Preprint (June 2022).