Research

Current position

Since September 2011, I am a research fellow (Wissenschaftlicher Mitarbeiterin) at the Mathematical Institute of the University of Münster, Germany. I work within the research group of Professor Urs Hartl.

From January to May 2012, I am also a post-doctoral fellow at Brown University in the new Institute for Computational and Experimental Research in Mathematics (ICERM). This stay is part of the semester program Complex and Arithmetic Dynamics.

Before that...

I received my doctorate degree in Mathematics from University Paris 7 in November 2008.

From December 2008 to August 2009, I was a postdoctoral researcher at the Department of Mathematics of the Universität des Saarlandes (Saarbrücken, Germany) in the research group of Professor Ernst Gekeler.

In 2009-2011, I was a post-doctoral fellow of the European Post-Doctoral Institute, based at IHÉS. My itinerary was as follows:

• from September 2009 to July 2010: Centre de Recerca Matemàtica, research programme Arithmetic Geometry (organizers: F. Bars, L. Dieulefait, V. Rotger)
• from August 2010 to October 2010: Institut des Hautes Études Scientifiques, Bures-sur-Yvette, France
• from November 2010 to August 2011: Max-Planck-Institut für Mathematik, Bonn, Germany.

Here is a curriculum vitae in English (French version).

Research interests

My research interests include number theory, arithmetic geometry and arithmetic of function field of positive characteristic. I am currently working on Drinfeld modules, Drinfeld modular curves, automorphic forms, modular symbols for F_q(T), Drinfeld modular forms.

What are Drinfeld modules useful for? The answer in this short video from the TV series 24 (season 4, episode 11). Also available in French dubbed version.

Publications

• Torsion des modules de Drinfeld de rang 2 et formes modulaires de Drinfeld (in French) - C. R. Math. Acad. Sci. Paris 347 (2009), 705-708
  preliminary version in PDF - final version available online
• Sur les symboles modulaires de Manin-Teitelbaum pour F_q(T) (in French) - C. R. Math. Acad. Sci. Paris 347 (2009), 845-848
  preliminary version in PDF - final version available online
• Coefficients of Drinfeld modular forms and Hecke operators - Journal of Number Theory 131 (2011), 1435-1460.
  preliminary version in PDF - final version available online
• Torsion des modules de Drinfeld de rang 2 et formes modulaires de Drinfeld - to appear in Algebra and Number Theory
  extended version of the corresponding C.R.Math. with proofs and improvements (2011, 41 pages, in French) - preliminary version in PDF

Preprints

• Une base explicite de symboles modulaires sur les corps de fonctions (2011, 29 pages, in French)
  Submitted - Revised version, November 2, 2011.

PhD Thesis

Doctorate degree (thèse de doctorat) in Mathematics, University Paris 7. Prepared under the supervision of Prof. Loïc Merel, at the Institut de Mathématiques de Jussieu in the Number Theory group.

Title: Torsion rationnelle des modules de Drinfeld. Defended in November 2008.

• the thesis dissertation (135 pages, in French - version of December 28, 2008)
• the corresponding page on TEL (contains a summary in English)

Various texts

DEA (Master's thesis)

In 2003, I graduated from the DEA Méthodes algébriques of University Paris 6. My master thesis was entitled La torsion des modules de Drinfeld (d'après B. Poonen). This work was done under the supervision of Prof. Loïc Merel and was based on Bjorn Poonen's article Torsion in rank-1 Drinfeld modules and the uniform boundedness conjecture (1997). Here is my dissertation.

Some notes from my talks

• Les formes modulaires, la cinquième opération de l'arithmétique, May 16, 2007 - Séminaire doctorant Lambda, Institut de Mathématiques de Bordeaux, University Bordeaux 1, France. Notes from the talk.
• Le quotient d'enroulement de la jacobienne de la courbe modulaire de Drinfeld X₀(N), June 7, 2006 - Colloque Jeunes Chercheurs en théorie des nombres 2006, Rennes, France. Notes from the talk.
• La torsion rationnelle des courbes elliptiques sur les corps de nombres (d'après Mazur, Kamienny, Merel), February 2006 - two talks at the number theory student seminar, Institut de Mathématiques de Jussieu, Paris, France. Notes from the talks.
• Introduction aux modules de Drinfeld, three talks at the number theory student seminar, fall 2003, Institut de Mathématiques de Jussieu, Paris, France. Notes from the talks.

Forthcoming events

• Semester Complex and Arithmetic Dynamics, ICERM, Brown University, January 30 - May 4, 2012. More details about the conferences on the webpage of the program.
• Conference on Number Theory, University of Göttingen, Germany, August 12 - 18, 2012. The conference will follow a summer school on number theory and cryptography, organised by the Mathematics Department of the Pennsylvania State University and the Institute of Mathematics of the University of Göttingen.

Passed events

• September 2009 - July 2010: Research Programme in Arithmetic Geometry, Centre de Recerca Matemàtica, Barcelona, Spain.
• April 13 to 17, 2011: Workshop on the Arithmetic of Function Fields, Imperial College London.
• June 20 to 22, 2011: XXIIèmes Rencontres Arithmétiques de Caen.
• June 24 to 31, 2011 : Mathematische Arbeitstagung 2011, MPIM, Bonn.
• August 16 to 19, 2011 : The Arithmetic of Function Fields and Related Topics, Dongguk University, Gyeongju, Korea.
• September 5 to 8, 2011: Conference Computations with Modular Forms 2011, University Heidelberg.
• Conference Number Theory and its applications, CIRM (Marseille, France) - January 16 - 20, 2012.

Links

• La Guilde des Doctorants, informations and advices for Ph.D. students, in French.
• James Milne's homepage and his lecture notes.
• Some electronical mathematical libraries: Gallica and Numdam (in French), Emani.
• From the celebrated PhD Comics: the Grad student Call of the Wild and the Grad student etiquette.