Dr. Benjamin Collas
Since 2015, I am a Principal Investigator in the research program SPP1786 on homotopy theory and algebraic geometry coordinated by M. Levine; attached to the Zahlentheorie Lehrstuhl of Prof. Dr. Michael Dettweiler.
My research interests focus on various aspects of the Arithmetic Geometry of moduli spaces of curves; 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 hyperplane arrangements 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.
- Hurwitz Stacks of Groups Extensions and Irreducibility, 2017. With S. Maugeais (final stage, 26 pages).
- On Galois Action on Stack Inertia of Moduli Spaces of Curves, 2014. With S. Maugeais (submitted) [PDF].
- Composantes irréductibles de lieux spéciaux d'espaces de modules de courbes, action galoisienne en genre quelconque, Annales de l'Institut Fourier, 2015. With S. Maugeais.
- 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.
- 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.
- WWU Munster Germany - AG Leray Topology (2012-14). I spent two years in Prof. M. S. Weiss' team getting familiar with recent developments in Algebraic Topology. I was the organizer of the Leray Oberseminar (russian style, 4 hours long), see Archives of the Leray and the Operads in Muenster subseminar.
- Université du Maine France (2011-12).
- Institut de Mathématiques de Jussieu France - Analyse Algébrique (2007-11).
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