A two-way study of operator algebras and discrete groups

2010 Fiscal Year Self-evaluation Report

• 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, 大学院・数理科学研究科, 准教授 (60323466)
• Project Period (FY): 2008 – 2010
• Keywords: 作用素環 / 離散群 / 関数解析

Research Abstract

(1)離散群、あるいはその測度空間への作用から作られるvon Neumann因子環の構造を調べ、分類する。
(2)離散群の解析的有限近似性について調べる。またその結果を(1)の因子環の研究や、グラフの距離空間への埋め込み可能性問題などに応用する。

Research Products

• [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] 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. 2 Pages: 271-280
• [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.)
• [Presentation] (2011)
  • Organizer: Embeddings workshop
  • Place of Presentation: Isaac Newton Institute
  • Year and Date: 20110100
• [Presentation] (2010)
  • Organizer: AMS Fall Western Section Meeting
  • Place of Presentation: UCLA
  • Year and Date: 20101000
• [Presentation] Actions and Invariants of Residually Finite Groups : Asymptotic Methods (2010)
  • Place of Presentation: Oberwolfach
  • Year and Date: 20100900
• [Presentation] (2010)
  • Organizer: Satellite Conference on Operator Algebras to ICM 2010
  • Place of Presentation: IMSc(Chennai)
  • Year and Date: 20100800
• [Presentation] (2010)
  • Organizer: Recent Developments in Operator Algebras
  • Place of Presentation: University of Tokyo
  • Year and Date: 20100600
• [Presentation] (2010)
  • Organizer: KOTAC 2010
  • Place of Presentation: Incheon
  • Year and Date: 20100600
• [Presentation] (2010)
  • Organizer: Noncommutative Geometry and Operator Algebras
  • Place of Presentation: Vanderbilt University
  • Year and Date: 20100500
• [Presentation] (2010)
  • Organizer: Danish-Norwegian Operator Algebra Seminar
  • Place of Presentation: University of Copenhagen
  • Year and Date: 20100400
• [Presentation] (2009)
  • Organizer: Operators and Operator Algebras
  • Place of Presentation: University of Edinburgh
  • Year and Date: 20091200
• [Presentation] Rigidity in cohomology, K-theory, geometry and ergodic theory (2009)
  • Place of Presentation: HIM(Bonn)
  • Year and Date: 20091100
• [Presentation] (2009)
  • Organizer: Geometry and Rigidity of Groups
  • Place of Presentation: Munster
  • Year and Date: 20090800
• [Presentation] (2009)
  • Organizer: Ergodic Theory of Group Actions
  • Place of Presentation: Gottingen
  • Year and Date: 20090800
• [Presentation] (2009)
  • Organizer: Operator Spaces and Approximation Properties of Discrete Groups
  • Place of Presentation: Texas A&M University
  • Year and Date: 20090800
• [Presentation] (2009)
  • Organizer: Noncommutative Lp spaces, operator spaces and applications
  • Place of Presentation: CIRM
  • Year and Date: 20090600
• [Presentation] (2009)
  • Organizer: von Neumann Algebras and Ergodic Theory
  • Place of Presentation: UCLA
  • Year and Date: 20090300
• [Presentation] (2009)
  • Organizer: von Neumann algebras, Ergodic theory and Geometric Group theory
  • Place of Presentation: IMSc(Chennai)
  • Year and Date: 20090200
• [Presentation] Harmonic analysis, operator algebras and representations (2008)
  • Place of Presentation: CIRM
  • Year and Date: 20081100
• [Presentation] (2008)
  • Organizer: von Neumann Algebras and Ergodic Theory of Group Actions
  • Place of Presentation: Oberwolfach
  • Year and Date: 20081000
• [Presentation] (2008)
  • Organizer: Analytic Properties of Infinite Groups
  • Place of Presentation: Geneve
  • Year and Date: 20080800
• [Presentation] Non-commutative Harmonic Analysis with Applications to Probability (2008)
  • Place of Presentation: B.dlewo
  • Year and Date: 20080800
• [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
• [Remarks] ウェブサイト
  • URL: http://www.ms.u-tokyo.ac.jp/~narutaka/