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.

Research

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.

Lecture

During the Summer semester, advanced lecture on ``Stack and homotopy algebraic geometry'', see the moodle page of the lecture for programme and references.

Publications

• Monodromy of Elliptic Curve Convolution and G2 Motives of Beauville type, 2018. With M. Dettweiler and S. Reiter (final stage, 26 pages, 12 figures and Magma code) [ArXiv].
• Hurwitz Stacks of Groups Extensions and Irreducibility, 2018. With S. Maugeais (17 pages), [ArXiv].
• 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.
  

Former positions

• 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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