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Collas, Benjamin

Research Institute for Mathematical Sciences (RIMS) Program-Specific Researcher

Collas, Benjamin
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    Last Updated :2025/05/01

    Basic Information

    Email Address

    • Email Address

      collas.benjamin.7jkyoto-u.ac.jp

    Academic Degree

    • 30 Jun. 2006
      Master's degree（University Paris 6）
    • 23 Sep. 2011
      Ph.D.（University Paris 6）

    Academic Resume (Graduate Schools)

    • University Paris 6, Institut de Mathematiques de Jussieu, 修了

    Academic Resume (Undergraduate School/Majors)

    • University Paris 7, 卒業
    • École Normale Supérieure Paris, Département de mathématiques et applications, Magisterien

    ID,URL

    Website(s) (URL(s))

    researchmap URL

    list
      Last Updated :2025/05/01

      Research

      Research Topics, Overview of the research

      • Research Topics

        Arithmetic anabelian geometry

      • Overview of the research

        My research subject is anabelian arithmetic geometry, mainly on the moduli stacks of curves and their stack inertia stratification. It includes simplical and homotopical algebraic geometry — i.e. model categories, Friedlander prospaces, and motivic considerations for stacks à la Morel-Voevodsky—, arithmetic geometry of curves — e.g. G-covers, irreducible components of Hurwitz spaces, étale fundamental group —, Grothendieck-Teichmüller theory — e.g. mapping class groups, pants decompositions, arithmetic of operads — , and Tannakian formalism in perverse sheaves.

      Research Areas

      • Natural sciences, Algebra

      Papers

      • Monodromy of elliptic curve convolution, seven-point sheaves of G2type, and motives of Beauville type
        Benjamin Collas; Michael Dettweiler; Stefan Reiter; Will Sawin
        Journal fur die Reine und Angewandte Mathematik, 01 Mar. 2022
      • Irreducible components of special loci in moduli spaces of curves, Galois action in general genus
        Benjamin Collas; Sylvain Maugeais
        Annales de l'Institut Fourier, 2015
      • Action of a Grothendieck-Teichmüller group on torsion elements of full teichmüller modular groups of genus one
        Benjamin Collas
        International Journal of Number Theory, May 2012
      • Action of the Grothendieck-Teichmüller group on torsion elements of full Teichmüller modular groups in genus zero
        Benjamin Collas
        Journal de Theorie des Nombres de Bordeaux, 2012

      Presentations

      • Galois-Teichmüller Theory: arithmetic geometric principles
        Benjamin Collas
        Grothendieck, a Multifarious Giant: Mathematics, Logic and Philosophy, 28 May 2022, Invited
      • Principles of Inter-universal Teichmüller Geometry
        Benjamin Collas
        Inter-universal Teichmüller Theory Summit 2021, 08 Sep. 2021, Invited
      • Simplicial and homotopical aspects in arithmetic geometry
        Benjamin Collas
        Homotopic & Geometric Galois Theory - Oberwolfach workshop, 11 Mar. 2021
      • Arithmetic of Perverse Sheaves and Moduli Spaces of Curves
        Benjamin Collas
        German Mathematical Society annual meeting, 17 Sep. 2020, Invited
      • Irreducibility in special loci with arithmetic motivations
        Benjamin Collas
        2nd Kyoto-Hefei Workshop on Arithmetic Geometry, 18 Aug. 2020, Invited
      • Arithmetic homotopic geometry, towards higher symmetries
        Benjamin Collas
        5th Kyoto Top Global University Mathematics Conference, 07 Feb. 2020, Invited
      • Moduli spaces of curves, arithmetic and operads
        Benjamin Collas
        Algebra Seminar Hiroshima University, 17 Jan. 2020
      • Arithmetic and motives for moduli stacks of curves
        Benjamin Collas
        Algebraic Number Theory and Related Topics 2019, 13 Dec. 2019, Invited
      • Galois and Tannakian Symmetries of Perverse Sheaves in Genus one
        Benjamin Collas
        Number Theory Seminar Kyoto University, 08 Nov. 2019
      • Moduli Stacks of Curves: Arithmetics and Motives
        Benjamin Collas
        Geometry and Topology Seminar Trondheim University, 05 Aug. 2019
      • Galois Arithmetics of Perverse Sheaves in Genus one
        Benjamin Collas
        Théorie de Galois Insulaire - XXIXèmes Rencontres Arithmétiques de Caen, 01 Jun. 2019, Invited
      • Arithmetic and Geometry of KZ-Equations
        Benjamin Collas
        Differential equations, Hodge theory and applications, Augsburg-Bayreuth-Chemnitz-Heidelberg Seminar, 09 May 2018
      • Moduli stack of curves: from arithmetic to motives
        Benjamin Collas
        Arithmetic Geometry and Symmetries around Galois and Fundamental Groups - Oberwolfach workshop, 16 Apr. 2018
      • Moduli Stack of Curves: from GT to Arithmetic
        Benjamin Collas
        Number Theory Seminar Osaka University, 02 Apr. 2018
      • Arithmetics of Moduli Spaces of Curves and Topological Approaches
        Benjamin Collas
        Low dimensional topology and number theory IX, 29 Mar. 2018, Invited
      • Arithmetic of Moduli Stacks of Curves
        Benjamin Collas
        Galois Seminar Upenn Philadelphia, 09 Feb. 2018
      • Stack Arithmetic of Moduli Spaces of Curves
        Benjamin Collas
        Workshop on Teichmüller and Grothendieck-Teichmüller theories, 25 Jul. 2017, Invited
      • Moduli Stack of Curves and Motivic Homotopy
        Benjamin Collas
        Jahrestagung of the DFG-SPP 1786, 21 Mar. 2017, Invited
      • Arithmetic and motivic considerations for the moduli stack of curves
        Benjamin Collas
        Workshop on Arithmetic and Geometry - TADMICAMT, 01 Sep. 2016, Invited
      • Champs de modules de courbes, considérations arithmétiques et motiviques
        Benjamin Collas
        Séminaire Arithmétique de Lille, 09 Jun. 2016
      • Arithmetics of Moduli Spaces of Curves
        Benjamin Collas
        Kollegseminar Kombinatorische Strukturen in der Geometrie, 03 May 2016, Invited
      • Stack Arithmetic of Moduli Spaces of Curves
        Benjamin Collas
        Arithmetic Geometry and Global Analysis Seminar Regensburg University, 22 Apr. 2016
      • Motivic homotopy considerations for Deligne Mumford stacks.
        Benjamin Collas
        Leray Topology Seminar WW Universität Münster, 01 Jun. 2015
      • Arithmetic of inertia in braids groups and Grothendieck-Teichmüller theory (towards a Grothendieck-Dynkin theory)
        Benjamin Collas
        Seminario Di Algebra, Topologia e Combinatoria Pisa University, 16 Apr. 2015
      • Stack inertia of moduli spaces of curves and Grothendieck-Teichmüller theory
        Benjamin Collas
        Colóquio de Geometria e Aritmética do Rio de Janeiro, 28 Mar. 2014, Invited
      • Espaces de modules de courbes, inerties et théories de Grothendieck-Teichmüller
        Benjamin Collas
        Femmes et Mathématiques – Algèbre et Géométrie, 14 Nov. 2012, Invited
      • Action de Grothendieck-Teichmüller sur inertie champêtre des espaces de modules de courbes
        Benjamin Collas
        Séminaire Géométrie Algébrique Université de Montpellier, 18 Oct. 2012
      • Grothendieck-Teichmüller groups : Galois and Hodge aspects II [GT and KZ]
        Benjamin Collas
        Arithmetic and Geometry of Picard-Fuchs Differential Equations, 21 Aug. 2012, Invited
      • Grothendieck-Teichmüller groups : Galois and Hodge aspects I [GT and Galois]
        Benjamin Collas
        Arithmetic and Geometry of Picard-Fuchs Differential Equations, 20 Aug. 2012, Invited
      • A glimpse of Grothendieck-Teichmüller theory
        Benjamin Collas
        Field Arithmetic Seminar Tel Aviv University, 06 Jun. 2012
      • Grothendieck-Teichmüller theory: Mapping class groups, braids and torsion
        Benjamin Collas
        Winter Braids II - Algebraic and Topological aspect of braids groups, 15 Dec. 2011, Invited
      • L'action de Grothendieck-Teichmüller sur l'inertie champêtre des espaces de modules de courbes est cyclotomique en genres zéro et un
        Benjamin Collas
        Séminaire Teich Université Paul Cézanne – FRURAM Marseille, 25 Nov. 2011
      • Galois group and Grothendieck-Teichmüller theory: Action on torsion-elements by cohomological methods
        Benjamin Collas
        Geometry and Arithmetic around Galois Theory, GTEM Summer School, 01 Jun. 2009, Invited

      External funds: others

      • Motivic Stack Inertia of Moduli Spaces of Curves
        Principal Investigator - Priority Program 1786
        Bayreuth university, Germany, Deutsche Forschnugsgemeinschaft
        From 01 Jun. 2015, To 31 May 2018
        Benjamin Collas
      list
        Last Updated :2025/05/01

        Academic, Social Contribution

        Committee Memberships

        • From Jan. 2023, To Present
          ``Arithmetic and Homotopic Galois Theory''(AHGT) International research network between France and Japan (main coordinator), RIMS Kyoto Japan and CNRS France

        Academic Contribution

        • Arithmetic Homotopy & Galois Theory, MFO-RIMS Tandem Workshop [Org.]
          Other
          B.Collas (RIMS Kyoto University, Japan), P. Dèbes (Lille, France), Y. Hoshi (RIMS Kyoto University, Japan), A. Mézard (ENS PSL, France), From 24 Sep. 2023, To 29 Sep. 2023
        • Arithmetic & Homotopic Galois Theory 2023 Workshop [Org.]
          Other
          B.Collas (RIMS Kyoto University, Japan), P. Dèbes (Lille, France), Y. Hoshi (RIMS Kyoto University, Japan), A. Mézard (ENS PSL, France), From 20 Mar. 2023, To 24 Mar. 2023
        • Inter-universal Teichmüller Theory Summit 2021 Workshop [Org.]
          Other
          Yuichiro Hoshi (RIMS, Kyoto University), Shinichi Mochizuki (RIMS, Kyoto University), Ivan Fesenko (The University of Nottingham, UK), Yuichiro Taguchi (Tokyo Institute of Technology), Benjamin Collas (RIMS, Kyoto University), From 07 Sep. 2021, To 10 Sep. 2021
        • Invitation to Inter-universal Teichmüller Theory Workshop [Org.]
          Other
          Yuichiro Hoshi (RIMS, Kyoto University), Shinichi Mochizuki (RIMS, Kyoto University), Ivan Fesenko (The University of Nottingham, UK), Yuichiro Taguchi (Tokyo Institute of Technology), Benjamin Collas (RIMS, Kyoto University), From 31 Aug. 2021, To 03 Sep. 2021
        • Combinatorial Anabelian Geometry and Related Topics Workshop [Org.]
          Other
          Yuichiro Hoshi (RIMS, Kyoto University), Shinichi Mochizuki (RIMS, Kyoto University), Ivan Fesenko (The University of Nottingham, UK), Arata Minamide (RIMS, Kyoto University), Shota Tsujimura (RIMS, Kyoto University), Benjamin Collas (RIMS, Kyoto University), From 05 Jul. 2021, To 09 Jul. 2021
        • Foundations and Perspectives of Anabelian Geometry Workshop [Org.]
          Other
          Ivan Fesenko (The University of Nottingham, UK), Arata Minamide (RIMS, Kyoto University), Fucheng Tan (RIMS, Kyoto University), Benjamin Collas (RIMS, Kyoto University), From 28 Jun. 2021, To 02 Jul. 2021
        • Homotopic and Geometric Galois Theory - Oberwolfach Workshop [Org.]
          Other
          Benjamin Collas; with Pierre Dèbes (Lille, FR), Hiroaki Nakamura (Osaka, JP) and Jakob Stix (Frankfurt, GE), From 07 Mar. 2021, To 21 Mar. 2021
        • Arithmetic Geometry and Symmetries around Galois and Fundamental Groups - Oberwolfach Workshop [Org.]
          Other
          Benjamin Collas; with Pierre Dèbes (Lille, FR) and Mike Fried (Irvine, US), From 15 Apr. 2018, To 21 Apr. 2018
        • Promenade in Inter-Universal Teichmüller Theory, RIMS Kyoto - Lille Seminar [Org.]
          Other
          Benjamin Collas; with Pierre Dèbes and Benoit Fresse (Lille, FR), From 24 Sep. 2020, To 22 Apr. 2021
        • Homotopical Arithmetic Geometry Seminar - 7 Topics - 七福話, RIMS Kyoto Seminar [Org.]
          Other
          Benjamin Collas; with Koichiro Sawada (RIMS, JP), From 06 Oct. 2020, To 14 Oct. 2020
        • Homotopical Anabelian Geometry, RIMS Kyoto Seminar [Org.]
          Other
          Benjamin Collas, From 17 Oct. 2019, To 16 Mar. 2020

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