I am a Principal Investigator in the research program SPP1786 on homotopy theory and algebraic geometry coordinated by M. Levine; attached to Michael Dettweiler's chair of Number Theory at Bayreuth Universität in Germany. My previous position was with Michael Weiss' Leray AG in Algebraic Topology at WW Universität Münster. My PhD has been supervised by Leila Schneps at the Institut of Mathematics of Jussieu - PRG - Paris 6 University Pierre and Marie Curie in the group Analyse Algébrique, where I was also a member of the european network GTEM (Galois Theory and Explicit Methods).
My research interests focus on the Arithmetic Geometry of moduli spaces of curves, and more specially on properties related to the stack inertia. My work deals with both groups theoretic aspects -- with properties of mapping class groups, (generalized) braids groups, bonté or Lanne's T-functor cohomological properties -- and geometric aspects -- with G-covers, deformations functors and components of stratifications. My motivations comes from the intertwining of geometry and group theory as for example in Grothendieck-Teichmüller theory, or the study of hyperplans arrangments and Dynkin lego.
I rencently turned my interest towards simplicial and homotopical methods (in relation with the proalgebraic side of the theory and the mixed Tate motives) as developed in Morel-Voevodsky's motivic homotopy theory. See here for a selection of talks by topics and there for my participation to conferences.
Keywords. arithmetic geometry, Grothendieck-Teichmüller theory, mapping class group, stack of moduli spaces of curves and G-covers, group cohomology, generalized braid groups, hyperplans arrangments, Dynkin diagrams, stable and unstable motivic model category, etale topology type.
- On Galois Action on Stack Inertia of Moduli Spaces of Curves, 2014 (25 pages), with S. Maugeais, [PDF].
- Action of the Grothendieck-Teichmüller group on torsion elements of full Teichmüller modular groups in genus zero, Journal de Théorie des Nombres de Bordeaux, vol.24, Iss.3, 2012 [PDF].
- Action of a Grothendieck-Teichmüller group on torsion elements of full Teichmüller modular groups in genus one, International Journal of Number Theory, vol.8, Iss.3, 2012 [PDF].
- Composantes irréductibles de lieux spéciaux d'espaces de modules de courbes, action galoisienne en genre quelconque, Annales de l'Institut Fourier, 2014 [PDF], with S. Maugeais.
- B. Collas, Mathématiques pour le L3 - Analyse, chapitre Analyse complexe d'une variable, Pearson Education, 2009. Chapitre 25