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Geometric group theory and metric embedding

Research Project

Project/Area Number 23244005
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionKyoto University (2012-2015)
Tohoku University (2011)

Principal Investigator

Fujiwara Koji  京都大学, 理学(系)研究科(研究院), 教授 (60229078)

Co-Investigator(Kenkyū-buntansha) OZAWA Narutaka  京都大学, 数理解析研究所, 教授 (60323466)
SHIOYA Takashi  東北大学, 理学(系)研究科(研究院), 教授 (90235507)
KAWAZUMI Nariya  東京大学, 数理(科)学研究科(研究院), 准教授 (30214646)
AKUTAGAWA Kazuo  東北大学, 大学院・情報科学研究科, 教授 (80192920)
Project Period (FY) 2011-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥47,840,000 (Direct Cost: ¥36,800,000、Indirect Cost: ¥11,040,000)
Fiscal Year 2015: ¥9,360,000 (Direct Cost: ¥7,200,000、Indirect Cost: ¥2,160,000)
Fiscal Year 2014: ¥9,880,000 (Direct Cost: ¥7,600,000、Indirect Cost: ¥2,280,000)
Fiscal Year 2013: ¥9,490,000 (Direct Cost: ¥7,300,000、Indirect Cost: ¥2,190,000)
Fiscal Year 2012: ¥10,790,000 (Direct Cost: ¥8,300,000、Indirect Cost: ¥2,490,000)
Fiscal Year 2011: ¥8,320,000 (Direct Cost: ¥6,400,000、Indirect Cost: ¥1,920,000)
Keywords幾何学的群論 / 双曲群 / 写像類群 / 作用素環論 / アレクサンドロフ空間 / 擬準同型 / 区間交換写像 / 幾何学 / 離散群論 / 測度集中 / simplicial volume / hyperbolic manifold / random groups / cat (0) cube complex / Alexandrov spaces / quasi-homomorphisms / p-harmonic map
Outline of Final Research Achievements

Fujiwara found a new method to embed certain discrete groups into a finite product of hyperbolic graphs in his joint work with Bestvina and Bromberg, and obtained important applications. Ozawa made a significant progress on the study of C*-algebra of discrete amenable groups, and also quasi-homomorphisms into non-commutative groups. Shioya found an important result on the asymptotics of the first eigen value of Laplacians on Alexandrov spaces.

Report

(5 results)
  • 2015 Final Research Report ( PDF )
  • 2014 Annual Research Report
  • 2013 Annual Research Report
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • Research Products

    (55 results)

All 2015 2014 2013 2012 2011 Other

All Journal Article (20 results) (of which Peer Reviewed: 19 results,  Open Access: 2 results,  Acknowledgement Compliant: 5 results) Presentation (34 results) (of which Invited: 26 results) Remarks (1 results)

  • [Journal Article] Asymptotically isometric metrics on relatively hyperbolic groups and marked length spectrum2015

    • Author(s)
      K. Fujiwara
    • Journal Title

      J. Topol. Anal.

      Volume: 7 Issue: 02 Pages: 345-359

    • DOI

      10.1142/s1793525315500132

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Constructing group actions on quasi-trees and applications to mapping class groups2014

    • Author(s)
      M. Bestvina, K. Bromberg and K. Fujiwara
    • Journal Title

      Publ. IHES

      Volume: Published online Issue: 1 Pages: 1-64

    • DOI

      10.1007/s10240-014-0067-4

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Counting subgraphs in hyperbolic graphs with symmetry.2014

    • Author(s)
      Calegari, K. Fujiwara,
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: -

    • NAID

      130005094188

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Subgroups generated by two pseudo-Anosov elements in a mapping class group. II. Uniform bound on exponents.2014

    • Author(s)
      K. Fujiwara.
    • Journal Title

      Trans. Amer. Math Soc.

      Volume: -

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Free Banach spaces and the approximation properties.2014

    • Author(s)
      G. Godefroy and N. Ozawa;
    • Journal Title

      Proc. Amer. Math. Soc

      Volume: 142 Issue: 5 Pages: 1681-1687

    • DOI

      10.1090/s0002-9939-2014-11933-2

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Free groups of interval exchange transformations are rare2013

    • Author(s)
      Dahmani, Francois; Fujiwara, Koji; Guirardel, Vincent
    • Journal Title

      Groups Geom. Dyn.

      Volume: 7 no. 4, . Pages: 883-910

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Shearing coordinates and convexity of length functions on Teichmüller space.2013

    • Author(s)
      Bestvina, M.; Bromberg, K.; Fujiwara, K.; Souto, J.
    • Journal Title

      Amer. J. Math.

      Volume: 135 no. 6 Pages: 1449-1476

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Geometry of the Funk metric on Weil-Petersson spaces.2013

    • Author(s)
      Fujiwara, Koji
    • Journal Title

      Math. Z

      Volume: 274no. 1-2 Pages: 647-665

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] A quantitative version of the commutator theorem for zero trace matrices2013

    • Author(s)
      W. B. Johnson, N. Ozawa, and G. Schechtman;.
    • Journal Title

      Proc. Nat. Acad. Sci.

      Volume: 110 Issue: 48 Pages: 19251-19255

    • DOI

      10.1073/pnas.1202411109

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Tsirelson's problem and asymptotically commuting unitary matrices.2013

    • Author(s)
      N. Ozawa;
    • Journal Title

      J. Math. Phys

      Volume: 54 Issue: 3 Pages: 1-8

    • DOI

      10.1063/1.4795391

    • NAID

      120005244650

    • Related Report
      2013 Annual Research Report 2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] About the Connes Embedding Conjecture---algebraic approaches---.2013

    • Author(s)
      N. Ozawa
    • Journal Title

      Jpn. J. Math

      Volume: 8 Issue: 1 Pages: 147-183

    • DOI

      10.1007/s11537-013-1280-5

    • Related Report
      2013 Annual Research Report 2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Dixmier approximation and symmetric amenability for C*-algebras.2013

    • Author(s)
      N. Ozawa; Dixmier approximation and symmetric amenability for C*-algebras.
    • Journal Title

      J. Math. Sci. Univ. Tokyo

      Volume: 20

    • NAID

      120005678242

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Concentration, Ricci curvature, and eigenvalues of Laplacian.2013

    • Author(s)
      Funano, Kei; Shioya, Takashi
    • Journal Title

      Geom. Funct. Anal.

      Volume: 23no. 3

    • Related Report
      2013 Annual Research Report
  • [Journal Article] Geometry of the Funk metric on Weil-Petersson spaces2013

    • Author(s)
      Koji Fujiwara
    • Journal Title

      Math. Z

      Volume: 274(1-2) Issue: 1-2 Pages: 647-665

    • DOI

      10.1007/s00209-012-1089-6

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Random groups have fixed points on CAT(0) cube complexes2012

    • Author(s)
      Koji Fujiwara and Tetsu Toyoda (K. Fujiwara)
    • Journal Title

      Proc. Amer. Math. Soc.

      Volume: 140 Issue: 3 Pages: 1023-1031

    • DOI

      10.1090/s0002-9939-2011-11343-1

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Random groups have fixed points on CAT(0) cube complexes2012

    • Author(s)
      Koji Fujiwara, Tetsu Toyoda
    • Journal Title

      Journal : Proc.Amer.Math.Soc.

      Volume: 140 Pages: 1023-1031

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Simplicial volume and fillings of hyperbolic manifolds2011

    • Author(s)
      Fujiwara, Koji; Manning, Jason Fox
    • Journal Title

      Algebr.Geom.Topol.

      Volume: 11, no.4 Pages: 2237-2264

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Geometric analysis on Alexandrov spaces2011

    • Author(s)
      Shioya, Takashi
    • Journal Title

      Sugaku Expositions

      Volume: 24 no.2 Pages: 145-167

    • NAID

      130004558881

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A topological splitting theorem for weighted Alexandrov spaces2011

    • Author(s)
      Kuwae, Kazuhiro; Shioya, Takashi
    • Journal Title

      Tohoku Math.J.(2)

      Volume: 63、no.1 Pages: 59-76

    • NAID

      110008425969

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Quasi-homomorphism rigidity with non-commutative targets2011

    • Author(s)
      Ozawa, Narutaka
    • Journal Title

      J.Reine Angew.Math.

      Volume: 655 Pages: 89-104

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Presentation] Stable commutator length on mapping class groups2014

    • Author(s)
      koji fujiwara
    • Organizer
      Geometric and Combinatorial Group Theory In honor of Eliyahu Rips workshop,
    • Place of Presentation
      Hebrew U, Israel.
    • Year and Date
      2014-12-18
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Noncommutative real algebraic geometry of Kazhdan's property (T)2014

    • Author(s)
      narutaka ozawa
    • Organizer
      Arithmetic and allied subjects on the banks of the Neva,
    • Place of Presentation
      オイラー国際数学研究所(ロシア)
    • Year and Date
      2014-11-01
    • Related Report
      2014 Annual Research Report
  • [Presentation] Asymptotically isometric metrics on hyperbolic groups2014

    • Author(s)
      koji fujiwara
    • Organizer
      The 10th Geometry conference for the friendship between China and Japan.
    • Place of Presentation
      Fudan University, China.
    • Year and Date
      2014-09-08
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Quasi-homomorphisms into non-commutative groups2014

    • Author(s)
      koji fujiwara
    • Organizer
      "Geometry on Groups and Spaces" ICM Satellite Conference on Geometric Group Theory & Geometric Structures, .
    • Place of Presentation
      KAIST, Daejeon, Korea
    • Year and Date
      2014-08-09
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Elementary amenable groups are quasidiagonal2014

    • Author(s)
      narutaka ozawa
    • Organizer
      Operator Algebras and Applications (ICM Satellite Conference),
    • Place of Presentation
      清風(韓国),
    • Year and Date
      2014-08-01
    • Related Report
      2014 Annual Research Report
  • [Presentation] Approximation Properties for Group C*-Algebras2014

    • Author(s)
      narutaka ozawa
    • Organizer
      Banach and Operator Algebras over Groups,
    • Place of Presentation
      フィールズ研究所(カナダ)
    • Year and Date
      2014-04-01
    • Related Report
      2014 Annual Research Report
  • [Presentation] Quasi-homomorphisms into non-commutative groups.2014

    • Author(s)
      koji fujiwara
    • Organizer
      Geometry of groups seminar, U Orsay.
    • Place of Presentation
      IHP, France.
    • Year and Date
      2014-03-14
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Quasi-homomorphisms into non-commutative groups.2014

    • Author(s)
      koji fujiwara
    • Organizer
      New Trends in Teichmuller Theory and Mapping Class
    • Place of Presentation
      . Oberwolfach, Germany.
    • Year and Date
      2014-02-12
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] An amenable operator algebra which is not a C*-algebra2013

    • Author(s)
      narutaka ozawa
    • Organizer
      Operator Algebras and Operator Theory Seminar, ,
    • Place of Presentation
      ソウル国立大学(韓国)
    • Year and Date
      2013-11-01
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] "Group actions on quasi-trees".2013

    • Author(s)
      koji fujiwara
    • Organizer
      日本数学会 企画特別講演 (愛媛大9月)
    • Place of Presentation
      愛媛大
    • Year and Date
      2013-09-27
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] "Group actions on quasi-trees and application".2013

    • Author(s)
      koji fujiwara
    • Organizer
      The XXIInd Rolf Nevanlinna Colloquim
    • Place of Presentation
      Helsinki.
    • Year and Date
      2013-08-09
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] "Group actions on quasi-trees".2013

    • Author(s)
      koji fujiwara
    • Organizer
      Differentialgeometrie im Grossen.
    • Place of Presentation
      Oberwolfach, Germany.
    • Year and Date
      2013-07-04
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Making bridges among long islands.2013

    • Author(s)
      koji fujiwara
    • Organizer
      "Geometric Structures in Group Theory".
    • Place of Presentation
      Oberwolfach, Germany.
    • Year and Date
      2013-06-05
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Group actions on quasi-trees (3 lectures).2012

    • Author(s)
      Koji Fujiwara
    • Organizer
      The 10th KAIST Geometric Topology Fair
    • Place of Presentation
      KIAS . Korea.
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Introduction to Connes' embedding problem2012

    • Author(s)
      N. Ozawa
    • Organizer
      Workshop on Connes' Embedding Conjecture
    • Place of Presentation
      Neuchatel (Switzerland)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Concentration of metric measure spaces2012

    • Author(s)
      T. Shioya
    • Organizer
      Analysis and Geometry in Metric Measure Spaces,
    • Place of Presentation
      Pisa, Italy
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Group actions on quasi-trees and quasi-cocycles2011

    • Author(s)
      Koji Fujiwara
    • Organizer
      Geometric and measured group theory
    • Place of Presentation
      Institut Henri Poincare, Paris, France(招待講演)
    • Year and Date
      2011-07-08
    • Related Report
      2011 Annual Research Report
  • [Presentation] Simplicial volume and fillings of hyperbolic manifolds2011

    • Author(s)
      Koji Fujiwara
    • Organizer
      Dubrovnik VII--Geometric Topology
    • Place of Presentation
      Dubrobnik, Croatia(招待講演)
    • Year and Date
      2011-06-27
    • Related Report
      2011 Annual Research Report
  • [Presentation] Subgroups of interval exchange transformations2011

    • Author(s)
      Koji Fujiwara
    • Organizer
      Geometric Group Theory
    • Place of Presentation
      Technion, Haifa, Israel(招待講演)
    • Year and Date
      2011-06-22
    • Related Report
      2011 Annual Research Report
  • [Presentation] Quasi-homomorphisms on groups and rank-rigidity2011

    • Author(s)
      Koji Fujiwara
    • Organizer
      Bonner Geometrietage (Ballmann's 60th birthday conference)
    • Place of Presentation
      MPI, Bonn, Germany(招待講演)
    • Year and Date
      2011-04-12
    • Related Report
      2011 Annual Research Report
  • [Presentation] Growth of groups

    • Author(s)
      Koji Fujiwara
    • Organizer
      Intelligence of Low-dimensional Topology
    • Place of Presentation
      RIMS, Kyoto.
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Quasi-trees and quasi-cocycles

    • Author(s)
      Koji Fujiwara
    • Organizer
      Topology and functional analysis
    • Place of Presentation
      Fudan University, Shanghai, China.
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Quasi-cocycles on free groups to uniformly convex Banach spaces

    • Author(s)
      Koji Fujiwara
    • Organizer
      Conference on Geometry
    • Place of Presentation
      RIMS, Kyoto
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Quasi-cocycles on free groups to uniformly convex Banach spaces

    • Author(s)
      Koji Fujiwara
    • Organizer
      Symplecctic geometry, geometric group theory and dynamics
    • Place of Presentation
      Obervolfach, Germany.
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Quasi-cocycles on free groups to uniformly convex Banach spaces

    • Author(s)
      Koji Fujiwara
    • Organizer
      Geometric and combinatorial group theory with applications (GAGTA-6)
    • Place of Presentation
      Dusseldorf, Germany
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Group actions on quasi-trees

    • Author(s)
      Koji Fujiwara
    • Organizer
      Discrete Geometric Analysis
    • Place of Presentation
      RIMS, Kyoto.
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Negative curvature in discrete groups

    • Author(s)
      Koji Fujiwara
    • Organizer
      第18回複素幾何シンポジウム
    • Place of Presentation
      菅平
    • Related Report
      2012 Annual Research Report
  • [Presentation] Group actions on quasi-trees.

    • Author(s)
      Koji Fujiwara
    • Organizer
      Cohomological methods in Goemetric group theory
    • Place of Presentation
      Banff International Research Station, Banff, Canada.
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Survey on the classification of von Neumann factors of type II_1

    • Author(s)
      N. Ozawa
    • Organizer
      Australian Mathematical Society 56th Annual Meeting
    • Place of Presentation
      Ballarat, Australia
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Survey on the classification of von Neumann factors of type II_1

    • Author(s)
      N. Ozawa
    • Organizer
      Harmonic Analysis, Operator Algebras and Representations,
    • Place of Presentation
      Luminy, France
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Quantum correlations and Tsirelson's problem

    • Author(s)
      N. Ozawa
    • Organizer
      AmenAbility
    • Place of Presentation
      Lausanne, switzerland
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Quantum correlations and Tsirelson's problem

    • Author(s)
      N. Ozawa
    • Organizer
      C*-Algebras and Noncommutative Dynamics
    • Place of Presentation
      Sde Boker (Israel)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Metric measure geometry for high-dimensional spaces

    • Author(s)
      T. Shioya
    • Organizer
      リーマン幾何と幾何解析
    • Place of Presentation
      筑波大
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Metric measure geometry of high-dimensional spaces

    • Author(s)
      T. Shioya
    • Organizer
      The 5th GCOE Internal Symposium on "Weaving Science Web beyond Particle-Matter Hierarchy"
    • Place of Presentation
      東北大
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Remarks]

    • URL

      http://www.math.is.tohoku.ac.jp/~fujiwara/

    • Related Report
      2011 Annual Research Report

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Published: 2011-04-06   Modified: 2019-07-29  

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