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Large scale structure of metric spaces from the viewpointo of operator algebras

Research Project

Project/Area Number 26870598
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Geometry
Basic analysis
Research InstitutionNiigata University

Principal Investigator

Sako Hiroki  新潟大学, 自然科学系, 准教授 (70708338)

Project Period (FY) 2014-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Keywords距離空間 / 大規模構造 / 作用素環 / 有限次元近似性質 / 距離空間の幾何学 / 非可換確率論 / 作用素環論 / 離散群論
Outline of Final Research Achievements

In this project, I examined mathematical research. The subject was large scale geometry on metric spaces. I tried to come up with new theorems related to the subject. There may be various ways in which we examine metric spaces. I decided to make use of knowledge on operator algebras. My knowledge on operator algebra has been utilized for this project. It has been pointed out that amenability on metric space corresponds to finite dimensional approximation property on operator algebras. In this project, I tried to generalize such kind of correspondence.

Report

(5 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (13 results)

All 2018 2016 2015 2014 2013 Other

All Journal Article (4 results) (of which Peer Reviewed: 4 results,  Open Access: 2 results,  Acknowledgement Compliant: 1 results) Presentation (8 results) (of which Int'l Joint Research: 1 results,  Invited: 1 results) Remarks (1 results)

  • [Journal Article] On a property of the simple random walk on Z2018

    • Author(s)
      N. Konno, H. Saigo and H. Sako
    • Journal Title

      Yokohama Mathematical Journal

      Volume: 63

    • NAID

      120006459863

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] The Arcsine law and an asymptotic behavior of orthogonal polynomials2016

    • Author(s)
      H. Saigo and H. Sako
    • Journal Title

      Annales de l'Institut Henri Poincare D

      Volume: 3 Issue: 4 Pages: 405-427

    • DOI

      10.4171/aihpd/34

    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] Group approximation in Cayley topology and coarse geometry, Part III: Geometric property (T)2015

    • Author(s)
      M. Mimura, N. Ozawa, H. Sako, and Y. Suzuki
    • Journal Title

      Algebraic and Geometric Topology

      Volume: 15 Issue: 2 Pages: 1067-1091

    • DOI

      10.2140/agt.2015.15.1067

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Property A and the operator norm localization property for discrete metric spaces2013

    • Author(s)
      Hiroki Sako
    • Journal Title

      Journal fur die reine und angewandte Mathematik

      Volume: (掲載確定) Issue: 690 Pages: 207-216

    • DOI

      10.1515/crelle-2012-0065

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Presentation] 一次元空間一様量子ウォークとリーマン面2018

    • Author(s)
      酒匂宏樹
    • Organizer
      「量子論にまつわる数学と数論の連携探索」, 早稲田大学
    • Related Report
      2017 Annual Research Report
  • [Presentation] Group approximation in Cayley topoloty and coarse geometry2016

    • Author(s)
      Hiroki Sako
    • Organizer
      Metric spaces Analysis, Embeddings into Banach Spaces, Applications
    • Place of Presentation
      Texas A&M University(アメリカ合衆国Texas州 College Station)
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] The arcsine law and an asymptotic behavior of orthogonal polynomials2015

    • Author(s)
      Hiroki Sako
    • Organizer
      Conference on non-commutative geometry and K-theory
    • Place of Presentation
      中華人民共和国 重慶大学
    • Year and Date
      2015-12-20
    • Related Report
      2015 Research-status Report
  • [Presentation] ケーリー位相と粗い幾何学 --- 第三部2015

    • Author(s)
      酒匂宏樹
    • Organizer
      日本数学会秋季総合分科会 幾何学分科会
    • Place of Presentation
      京都産業大学
    • Year and Date
      2015-09-16
    • Related Report
      2015 Research-status Report
  • [Presentation] 逆正弦法則と直交多項式の漸近挙動2015

    • Author(s)
      酒匂宏樹
    • Organizer
      日本数学会秋季総合分科会 函数解析分科会
    • Place of Presentation
      京都産業大学
    • Year and Date
      2015-09-14
    • Related Report
      2015 Research-status Report
  • [Presentation] 逆正弦法則と直交多項式の漸近挙動2015

    • Author(s)
      酒匂宏樹
    • Organizer
      実函数函数解析合同シンポジウム
    • Place of Presentation
      神奈川大学
    • Year and Date
      2015-09-02
    • Related Report
      2015 Research-status Report
  • [Presentation] Sequences of finite metric spaces : amenability and connectivity2015

    • Author(s)
      Hiroki Sako
    • Organizer
      Conference ``Topics in Differencial Geometry and its Discretizations''
    • Place of Presentation
      WPI-AIMR, 東北大学
    • Year and Date
      2015-01-11
    • Related Report
      2014 Research-status Report
  • [Presentation] Coarse amenability for discrete metric spaces2014

    • Author(s)
      Hiroki Sako
    • Organizer
      Conference ``von Neumann Algebras and Ergodic Theory''
    • Place of Presentation
      University of California, Los Angeles
    • Year and Date
      2014-09-22
    • Related Report
      2014 Research-status Report
  • [Remarks] Research (Hiroki SAKO)

    • URL

      http://www1.hinocatv.ne.jp/sako-h/research/research.html

    • Related Report
      2014 Research-status Report

URL: 

Published: 2014-04-04   Modified: 2019-03-29  

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