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Universität Bayreuth
Mathematisches Institut
Lehrstuhl für Zahlentheorie
D-95440 Bayreuth, Germany.

Tel: +49 (0)921/55-3288

Office: NW II, Raum 734.

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SPP - Homotopy Theory and Algebraic Geometry.

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 focuses on various aspects of the Arithmetic Geometry of moduli stacks of curves in terms of the Deligne-Mumford and the stack inertia stratifications. My approach covers the topics of simplicial and homotopical algebraic geometry -- i.e. motivic considerations for stacks à la Morel-Voevodsky --, of the arithmetic of the geometry of curves -- e.g. G-covers, irreducible components of Hurwitz spaces, étale fundamental group --, methods from Grothendieck-Teichmüller theory -- e.g. mapping class groups, pants decompositions, Serre bonté --, and the arithmetic of operads -- in genus 0 via Friedlander étale topological type and prospaces.

Recent Activities

  • Visiting Osaka university and RIMS Kyoto (20.08 - 15.10), planed: 4 lectures on Arithmetic Homotopy of Moduli Stack of Curves;
  • Arithmetic and Homotopy of Moduli Stacks of Curves, in Oberwolfach's AG and Symmetries around Galois and Fundamental Groups;
  • Arithmetic of Moduli Stacks of Curves, at Upenn, US;
  • Moduli Stack of Curves: from GT to Arithmetic, at Osaka University, Japan;
  • Arithmetic of Operads of Moduli Spaces of Curves, at Temple University, US;
  • Arithmetic and Geometry of KZ-Equations, in Hypergeometric Differential Equations, Bayreuth-Chemnitz-Heidelberg Seminar.

See here for more talks by topics, or here for organization of conferences and seminars, and here for international invitations.


During the Summer semester 2018: advanced lecture on ``Stacks and homotopy algebraic geometry'', see the moodle page of the lecture for programme and references.



  • 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.



  • Mathématiques pour le L3 - Analyse, chapter ``Analyse complexe d'une variable'', Pearson Education, 2009. Chapitre 25

Former positions

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