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).

Research

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

• XXIXèmes Rencontres Arithmétiques de Caen (29.05 -03.06.19): "Field Arithmetic and Arithmetic Geometry" ;
• 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.

Lecture

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

Publications

Articles

• Monodromy of Elliptic Curve Convolution, Seven-point sheaves of G2-type, and Motives of Beauville type, 2018. With M. Dettweiler, S. Reiter and W. Sawin (v2, 26 pages, 12 figures) [ArXiv], [PDF].
• 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, 2018 (v1:2014). With S. Maugeais (submitted) [ArXiv], [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.
  

Proceedings

• Arithmetic Geometry and Symmetries around Galois and Fundamental Groups, Mini-Workshop MFO 2018 - Introduction of the organizers with P. Dèbes and M. Fried (7 pages).
• Arithmetic and Homotopy of Moduli Stacks of Curves, in Oberwolfach Reports - OWR Report (8 pages).

Book

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

Former positions

• WWU Munster Germany - AG Leray Topology. 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.
• Institut de Mathématiques de Jussieu France - Analyse Algébrique.

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