A two-way study of operator algebras and discrete groups

• Project/Area Number: 20684004
• Research Category: Grant-in-Aid for Young Scientists (A)
• Allocation Type: Single-year Grants
• Research Field: Global analysis
• Research Institution: The University of Tokyo (2008-2009, 2011); Kyoto University (2010)
• Principal Investigator: OZAWA Narutaka The University of Tokyo, 数理(科)学研究科(研究院), 准教授 (60323466)
• Project Period (FY): 2008 – 2010
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥6,110,000 (Direct Cost: ¥4,700,000、Indirect Cost: ¥1,410,000); Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2008: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
• Keywords: 作用素環 / 離散群 / 関数解析 / 関数解析学 / 作用素環論 / 離散群論 / 幾何学

Research Abstract

Ozawa studied the structure of von Neumann factors arising from discrete groups and their actions on probability spaces, and contributed to the classification theory of von Neumann factors. He also studied analytic approximation properties of discrete groups and applied them to the study of von Neumann factors and to the embedding problem of graphs into metric spaces.

Research Products

• [Journal Article] Examples of groups which are not weakly amenable (2012)
  • Author(s): N. Ozawa
  • Journal Title: Kyoto J. Math. Volume: 52 Pages: 333-344
  • Peer Reviewed
• [Journal Article] Quasi-homomorphism rigidity with noncom mutative targets (2011)
  • Author(s): N. Ozawa
  • Journal Title: J. Reine Angew. Math. Volume: 655 Pages: 89-104
  • Peer Reviewed
• [Journal Article] On Ulam stability (2011)
  • Author(s): M.Burger, N.Ozawa, A.Thom
  • Journal Title: Israel Journal of Mathematics Volume: (掲載確定)
  • Peer Reviewed
• [Journal Article] Examples of groups which are not weakly amenable (2011)
  • Author(s): N.Ozawa
  • Journal Title: Preprint Volume: (掲載確定)
• [Journal Article] Quasi-homomorphism rigidity with noncommutative targets (2011)
  • Author(s): N.Ozawa
  • Journal Title: J.reine angew.Math. Volume: (掲載確定)
  • Peer Reviewed
• [Journal Article] The Dixmier problem, lamplighters and Burnside groups. (2010)
  • Author(s): N. Ozawa and N. Monod
  • Journal Title: J. Funct. Anal. Volume: 258 Pages: 255-259
  • Peer Reviewed
• [Journal Article] On a class of II_1 factors with at most one Cartan subalgebra II. (2010)
  • Author(s): N. Ozawa and S. Popa
  • Journal Title: Amer. J. Math. Volume: 132 Pages: 841-866
  • Peer Reviewed
• [Journal Article] On a class of II_1 factors with at most one Cartan subalgebra. (2010)
  • Author(s): N. Ozawa and S. Popa
  • Journal Title: Ann. of Math. Volume: 172 Pages: 713-749
  • Peer Reviewed
• [Journal Article] The Dixmier problem, lamplighters and Burnside groups. (2010)
  • Author(s): N.Ozawa, N.Monod
  • Journal Title: J.Funct.Anal. 258 Pages: 255-259
• [Journal Article] On a class of II_1 factors with at most one Cartan subalgebra II. (2010)
  • Author(s): N.Ozawa, S.Popa
  • Journal Title: Amer.J.Math. 132 Pages: 841-866
• [Journal Article] On a class of II_1 factors with at most one Cartan subalgebra. (2010)
  • Author(s): N.Ozawa, S.Popa
  • Journal Title: Ann.of Math. 172 Pages: 713-749
• [Journal Article] The Dixmier problem, lamplighters and Burnside groups (2010)
  • Author(s): N.Monod, N.Ozawa
  • Journal Title: Journal of Functional Analysis 258 Pages: 255-259
  • Peer Reviewed
• [Journal Article] An example of a solid von Neumann algebra (2009)
  • Author(s): N. Ozawa
  • Journal Title: Hokkaido Math. J. Volume: 38 Pages: 557-561
  • Peer Reviewed
• [Journal Article] An example of a solid von Neumann algebra. (2009)
  • Author(s): N.Ozawa
  • Journal Title: Hokkaido Math.J. 38 Pages: 557-561
• [Journal Article] Weak amenability of hyperbolic groups (2008)
  • Author(s): N. Ozawa
  • Journal Title: Groups Geom. Dyn. Volume: 2 Pages: 271-280
  • Peer Reviewed
• [Journal Article] Weak amenability of hyperbolic groups. (2008)
  • Author(s): N.Ozawa
  • Journal Title: Groups Geom.Dyn. 2 Pages: 271-280
• [Journal Article] On Ulam stability
  • Author(s): M. Burger, N. Ozawa and A. Thom
  • Journal Title: Israel J. Math.
  • Peer Reviewed
• [Journal Article] On Ulam stability.
  • Author(s): M.Burger, N.Ozawa, A.Thom
  • Journal Title: Israel J.Math. (accepted)
• [Journal Article] Quasi-homomorphism rigidity with noncommutative targets.
  • Author(s): N.Ozawa
  • Journal Title: J.Reine Angew.Math. (to appear.)
• [Journal Article] Quasi-homomorphism rigidity with noncommutative targets
  • Author(s): N.Ozawa
  • Journal Title: Journal fur die reine und angewandte Mathematik (掲載決定済み, 掲載確定)
  • Peer Reviewed
• [Journal Article] An example of a solid von Neumann algebra
  • Author(s): N. OZAWA
  • Journal Title: Hokkaido Math. J. (accepted)
  • Peer Reviewed
• [Journal Article] On a class of II_I factors with at most one Cartan subalgebra
  • Author(s): N. OZAWA and S. POPA
  • Journal Title: Ann. of Math. (2) (accepted)
  • Peer Reviewed
• [Journal Article] On a class of II_I factors with at most one Cartan subalgebra II
  • Author(s): N. OZAWA and S. POPA
  • Journal Title: Preprint
• [Presentation] ME embeddings for groups (2011)
  • Author(s): N. Ozawa
  • Organizer: Embeddings workshop, Isaac Newton Institute
  • Year and Date: 2011-01-14
• [Presentation] (2011)
  • Organizer: Embeddings workshop
  • Place of Presentation: Isaac Newton Institute
• [Presentation] Survey on weak amenability for groups (2010)
  • Author(s): 小澤登高
  • Organizer: 関西作用素環セミナー
  • Place of Presentation: 福井県、芦原湯町
  • Year and Date: 2010-12-18
• [Presentation] Quasi-homomorphism rigidity with noncommutative targets (2010)
  • Author(s): N. Ozawa
  • Organizer: Satellite Conference on Operator Algebras to ICM 2010
  • Place of Presentation: IMSc(Chennai)
  • Year and Date: 2010-10-10
• [Presentation] Quasi-homomorphism rigidity with noncommutative targets (2010)
  • Author(s): N. Ozawa
  • Organizer: AMS Fall Western Section Meeting
  • Place of Presentation: UCLA
  • Year and Date: 2010-10-09
• [Presentation] Quasi-homomorphism rigidity with noncommutative targets (2010)
  • Author(s): N.Ozawa
  • Organizer: AMS Fall Western Section Meeting
  • Place of Presentation: UCLA(ロサンゼルス・アメリカ合衆国)
  • Year and Date: 2010-10-09
• [Presentation] Quasi-homomorphism rigidity with noncommutative targets (2010)
  • Author(s): N. Ozawa
  • Organizer: Actions and Invariants of Residually Finite Groups : Asymptotic Methods, Oberwolfach
  • Year and Date: 2010-09-09
• [Presentation] Group measure space von Neumann algebras and measure group theory (2010)
  • Author(s): N.Ozawa
  • Organizer: Actions and Invariants of Residually Finite Groups
  • Place of Presentation: 数学研究所・Oberwolfach(ドイツ)
  • Year and Date: 2010-09-09
• [Presentation] Quasi-homomorphism rigidity with noncommutative targets (2010)
  • Author(s): N.Ozawa
  • Organizer: Satellite Conference on Operator Algebras to ICM
  • Place of Presentation: 数理科学研究所・チェンナイ(インド)
  • Year and Date: 2010-08-10
• [Presentation] Quasi-homomorphism rigidity with noncommutative targets (2010)
  • Author(s): N. Ozawa
  • Organizer: Recent Developments in Operator Algebras
  • Place of Presentation: University of Tokyo
  • Year and Date: 2010-06-25
• [Presentation] Quasi-homomorphism rigidity with noncommutative targets (2010)
  • Author(s): N.Ozawa
  • Organizer: Recent Developments in Operator Algebras
  • Place of Presentation: 東京大学
  • Year and Date: 2010-06-25
• [Presentation] Dixmier's Similarity Problem (2010)
  • Author(s): N. Ozawa
  • Organizer: KOTAC 2010
  • Place of Presentation: Incheon
  • Year and Date: 2010-06-17
• [Presentation] Quasi-homomorphism rigidity with noncommutative targets (2010)
  • Author(s): N. Ozawa
  • Organizer: Danish-Norwegian Operator Algebra Seminar
  • Place of Presentation: University of Copenhagen
  • Year and Date: 2010-04-09
• [Presentation] Quasi-homomorphism rigidity with noncommutative targets (2010)
  • Author(s): N.Ozawa
  • Organizer: Danish-Norwegian Operator Algebra Seminar
  • Place of Presentation: コペンハーゲン大学(コペンハーゲン,デンマーク)
  • Year and Date: 2010-04-09
• [Presentation] Closable derivations on finite von Neumann algebras (2010)
  • Author(s): N. Ozawa
  • Organizer: Noncommutative Geometry and Operator Algebras
  • Place of Presentation: Vanderbilt University
• [Presentation] Actions and Invariants of Residually Finite Groups : Asymptotic Methods (2010)
  • Place of Presentation: Oberwolfach
• [Presentation] (2010)
  • Organizer: AMS Fall Western Section Meeting
  • Place of Presentation: UCLA
• [Presentation] (2010)
  • Organizer: Satellite Conference on Operator Algebras to ICM 2010
  • Place of Presentation: IMSc(Chennai)
• [Presentation] (2010)
  • Organizer: Recent Developments in Operator Algebras
  • Place of Presentation: University of Tokyo
• [Presentation] (2010)
  • Organizer: Noncommutative Geometry and Operator Algebras
  • Place of Presentation: Vanderbilt University
• [Presentation] (2010)
  • Organizer: Danish-Norwegian Operator Algebra Seminar
  • Place of Presentation: University of Copenhagen
• [Presentation] (2010)
  • Organizer: KOTAC 2010
  • Place of Presentation: Incheon
• [Presentation] Closable derivations on finite von Neumann algebras (3 hours) (2010)
  • Author(s): N.Ozawa
  • Organizer: Noncommutative Geometry and Operator Algebras
  • Place of Presentation: Vanderbilt University(ナッシュビル,アメリカ合衆国)
• [Presentation] Dixmier's Similarity Problem (2009)
  • Author(s): N. Ozawa
  • Organizer: Operators and Operator Algebras
  • Place of Presentation: University of Edinburgh
  • Year and Date: 2009-12-11
• [Presentation] Quasi-homomorphism rigidity with noncommutative targets (2009)
  • Author(s): N. Ozawa
  • Organizer: Rigidity in cohomology, K-theory, geometry and ergodic theory
  • Place of Presentation: HIM(Bonn)
  • Year and Date: 2009-11-23
• [Presentation] Dixmier's Similarity Problem (2009)
  • Author(s): N. Ozawa
  • Organizer: Geometry and Rigidity of Groups
  • Place of Presentation: Munster
  • Year and Date: 2009-08-28
• [Presentation] Dixmier's Similarity Problem (2009)
  • Author(s): N.Ozawa
  • Organizer: Geometry and Rigidity of Groups
  • Place of Presentation: Universitat Munster
  • Year and Date: 2009-08-28
• [Presentation] Dixmier's Similarity Problem (2009)
  • Author(s): N. Ozawa
  • Organizer: Noncommutative Lp spaces, operator spaces and applications
  • Place of Presentation: CIRM
  • Year and Date: 2009-06-08
• [Presentation] Dixmier's Similarity Problem (2009)
  • Author(s): N.Ozawa
  • Organizer: Noncommutative Lp spaces, operator spaces and applications
  • Place of Presentation: CIRM(Marseille)
  • Year and Date: 2009-06-08
• [Presentation] 群測度von Neumann環の分類 (2009)
  • Author(s): 小沢登高
  • Organizer: 日本数学会年会
  • Place of Presentation: 東京大学
  • Year and Date: 2009-03-27
• [Presentation] On a class of II_1 factors with at most one Cartan subalgebra (2009)
  • Author(s): N. Ozawa
  • Organizer: von Neumann Algebras and Ergodic Theory
  • Place of Presentation: UCLA
  • Year and Date: 2009-03-18
• [Presentation] On a class of II_1 factors with at most one Cartan subalgebra (2009)
  • Author(s): N. OZAWA
  • Organizer: von Neumann Algebras and Ergodic Theory
  • Place of Presentation: University of California, Los Angeles (アメリカ合衆国)
  • Year and Date: 2009-03-18
• [Presentation] Neumann algebras and ergodic theory of group actions (2009)
  • Author(s): N. Ozawa
  • Organizer: Ergodic Theory of Group Actions
  • Place of Presentation: Gottingen
• [Presentation] Hyperlinearity, sofic groups and applications to group theory (2009)
  • Author(s): N. Ozawa
  • Organizer: Operator Spaces and Approximation Properties of Discrete Groups
  • Place of Presentation: Texas A & M University
• [Presentation] Von Neumann algebras and ergodic theory of group actions (2009)
  • Author(s): N. Ozawa
  • Organizer: von Neumann algebras and Ergodic theory and Geometric Group theory
  • Place of Presentation: IMSc(Chennai)
• [Presentation] Rigidity in cohomology, K-theory, geometry and ergodic theory (2009)
  • Place of Presentation: HIM(Bonn)
• [Presentation] (2009)
  • Organizer: Operators and Operator Algebras
  • Place of Presentation: University of Edinburgh
• [Presentation] (2009)
  • Organizer: Geometry and Rigidity of Groups
  • Place of Presentation: Munster
• [Presentation] (2009)
  • Organizer: Ergodic Theory of Group Actions
  • Place of Presentation: Gottingen
• [Presentation] (2009)
  • Organizer: Operator Spaces and Approximation Properties of Discrete Groups
  • Place of Presentation: Texas A&M University
• [Presentation] (2009)
  • Organizer: Noncommutative Lp spaces, operator spaces and applications
  • Place of Presentation: CIRM
• [Presentation] (2009)
  • Organizer: von Neumann Algebras and Ergodic Theory
  • Place of Presentation: UCLA
• [Presentation] (2009)
  • Organizer: von Neumann algebras, Ergodic theory and Geometric Group theory
  • Place of Presentation: IMSc(Chennai)
• [Presentation] Hyperlinearity, sofic groups and applications to group theory(3 lectures) (2009)
  • Author(s): N.Ozawa
  • Organizer: Operator Spaces and Approximation Properties of Discrete Groups
  • Place of Presentation: Texas A&M University
• [Presentation] von Neumann algebras and ergodic theory(4 lectures) (2009)
  • Author(s): N.Ozawa
  • Organizer: Ergodic Theory of Group Actions
  • Place of Presentation: Gottingen University
• [Presentation] On a class of II_1 factors with at most one Cartan subalgebra (2008)
  • Author(s): N. Ozawa
  • Organizer: Harmonic analysis, operator algebras and representations
  • Place of Presentation: CIRM
  • Year and Date: 2008-11-10
• [Presentation] On a class of II_1 factors with at most one Cartan subalgebra (2008)
  • Author(s): N. OZAYA
  • Organizer: Harmonic analysis, operator algebras and representations
  • Place of Presentation: Centre International de Rencontres Mathematiques(フランス)
  • Year and Date: 2008-11-06
• [Presentation] On a class of II_1 factors with at most one Cartan subalgebra (2008)
  • Author(s): N. OZAWA
  • Organizer: von Neumann Algebras and Ergodic Theory of Group Actions
  • Place of Presentation: Mathematisches Forschungsinstitut Oberwolfach(ドイツ)
  • Year and Date: 2008-10-31
• [Presentation] On a class of II_1 factors with at most one Cartan subalgebra (2008)
  • Author(s): N. OZAWA
  • Organizer: Analytic Properties of Infinite Groups
  • Place of Presentation: University of Geneva(スイス)
  • Year and Date: 2008-08-25
• [Presentation] On a class of II_1 factors with at most one Cartan subalgebra (2008)
  • Author(s): N. OZAWA
  • Organizer: Non-commutative Harmonic Analysis with Applications to Probability
  • Place of Presentation: Banach Center at Bedlewo(ポーランド)
  • Year and Date: 2008-08-21
• [Presentation] On a class of II_1 factors with at most one Cartan subalgebra (2008)
  • Author(s): N. OZAWA
  • Organizer: Operator AlgebrasOynamics, and Classification
  • Place of Presentation: Texas A&M University (アメリカ合衆国)
  • Year and Date: 2008-08-08
• [Presentation] On a class of II_1 factors with at most one Cartan subalgebra (2008)
  • Author(s): N. Ozawa
  • Organizer: von Neumann Algebras and Ergodic Theory of Group Actions
  • Place of Presentation: Oberwolfach
• [Presentation] On a class of II_1 factors with at most one Cartan subalgebra (2008)
  • Author(s): N. Ozawa
  • Organizer: Analytic Properties of Infinite Groups
  • Place of Presentation: Geneve
• [Presentation] On a class of II_1 factors with at most one Cartan subalgebra (2008)
  • Author(s): N. Ozawa
  • Organizer: Non-commutative Harmonic Analysis with Applications to Probability
  • Place of Presentation: B. dlewo(Poland)
• [Presentation] Harmonic analysis, operator algebras and representations (2008)
  • Place of Presentation: CIRM
• [Presentation] (2008)
  • Organizer: von Neumann Algebras and Ergodic Theory of Group Actions
  • Place of Presentation: Oberwolfach
• [Presentation] (2008)
  • Organizer: Analytic Properties of Infinite Groups
  • Place of Presentation: Geneve
• [Presentation] Non-commutative Harmonic Analysis with Applications to Probability (2008)
  • Place of Presentation: B.dlewo
• [Book] C-algebras and finite-dimensional approximations Graduate Studies in Mathematics (2008)
  • Author(s): N. Brown and N. Ozawa
  • Total Pages: 509
  • Publisher: American Mathematical Society
• [Book] American Mathematical Society(C*-algebras and finite-dimensional approximations.Graduate Studies in Mathematics,88) (2008)
  • Author(s): N.Brown, N.Ozawa
  • Total Pages: 509
• [Book] C*-algebras and finite-dimensional approximations (2008)
  • Author(s): N.P. BROWN and N. OZAWA
  • Total Pages: 509
  • Publisher: American Mathematical Society
• [Remarks] ウェブサイト
  • URL: http://www.kurims.kyoto-u.ac.jp/~narutaka/
• [Remarks] ウェブサイトでは自分の研究成果、研究紹介のほか、参加した研究集会の報告、講義録などを公開している。
• [Remarks] ウェブサイト
  • URL: http://www.ms.u-tokyo.ac.jp/~narutaka/
• [Remarks]
  • URL: http://www.ms.u-tokyo.ac.jp/~narutaka/
• [Remarks]
  • URL: http://www.ms.u-tokyo.ac.jp/~narutaka/
• [Remarks]
  • URL: http://www.ms.u-tokyo.ac.jp/~narutaka/