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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

Postdoctoral Researcher attached to the Zahlentheorie Lehrstuhl of Prof. Dr. Michael Dettweiler, previously Principal Investigator in the research program SPP1786 on homotopy theory and algebraic geometry coordinated by M. Levine (2015-18).


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): 5 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 (04.18);
  • Arithmetic of Moduli Stacks of Curves, at Upenn, US (03.18);
  • Moduli Stack of Curves: from GT to Arithmetic, at Osaka University, Japan (03.18);
  • Arithmetic of Operads of Moduli Spaces of Curves, at Temple University, US (03.18);
  • Arithmetic and Geometry of KZ-Equations, in Hypergeometric Differential Equations, Bayreuth-Chemnitz-Heidelberg Seminar (05.18).

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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