• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Discrete geometry and creation of 3 dimensional geometric models

Research Project

Project/Area Number 15K13434
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Geometry
Research InstitutionThe University of Tokyo

Principal Investigator

KOHNO Toshitake  東京大学, 大学院数理科学研究科, 教授 (80144111)

Project Period (FY) 2015-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords離散幾何学 / 定曲率曲面 / 極小曲面 / 代数曲面 / 特異点理論 / 可積分系 / 極限集合 / 離散データ / 単体分割 / モーデル・ヴェイユ格子 / 曲率
Outline of Final Research Achievements

In this research we developed a method to create extremely accurate 3 dimensional models of surfaces appearing in geometry and topology by curving metals. This method realized models much more accurate than those created by 3D printers. We also developed techniques realizing limit sets of discrete group and objects in singularity theory, foliation theory and integrable systems, which were difficult to create by previous methods. By adding data of normal direction to discrete point data sets and mesh, we realized accuracy of less than 1/100mm. Our research established a new interface for creating accurate 3 dimensional models.

Report

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

    (20 results)

All 2018 2017 2016 2015 2013 Other

All Journal Article (5 results) (of which Peer Reviewed: 5 results,  Acknowledgement Compliant: 2 results) Presentation (8 results) (of which Int'l Joint Research: 8 results,  Invited: 8 results) Book (1 results) Remarks (5 results) Funded Workshop (1 results)

  • [Journal Article] Quantum representations of braid groups and holonomy Lie algebras2017

    • Author(s)
      Toshitake Kohno
    • Journal Title

      Advanced Studies in Pure Mathematics

      Volume: 72 Pages: 117-144

    • Related Report
      2017 Annual Research Report 2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] Homological Representations of Braid Groups and the Space of Conformal Blocks2017

    • Author(s)
      Toshitake Kohno
    • Journal Title

      Springer INdAM Series

      Volume: 19 Pages: 427-442

    • DOI

      10.1007/978-3-319-58971-8_16

    • ISBN
      9783319589701, 9783319589718
    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Higher holonomy maps of formal homology connections and braid cobordisms2016

    • Author(s)
      Toshitake Kohno
    • Journal Title

      Journal of Knot Theory and Its Ramifications

      Volume: 26 Issue: 12 Pages: 1642007-1642007

    • DOI

      10.1142/s0218216516420074

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Higher holonomy maps of formal homology connections and braid cobordisms2016

    • Author(s)
      T. Kohno
    • Journal Title

      Journal of Knot Theory and Its Ramifications

      Volume: 未定

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Circle-valued Morse theory for complex hyperplane arrangements2013

    • Author(s)
      T. Kohno, A. Pajitnov
    • Journal Title

      Forum Mathematicum

      Volume: (Published on line) Issue: 4 Pages: 2113-2128

    • DOI

      10.1515/forum-2013-0032

    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Presentation] Local systems on configuration spaces, KZ connections and conformal blocks2018

    • Author(s)
      Toshitake Kohno
    • Organizer
      Topology of Arrangements and Representation Stability, Oberwolfach
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Higher category extensions of holonomy maps and representations of braid cobordims2018

    • Author(s)
      Toshitake Kohno
    • Organizer
      The 13th Algebra-Analysis-Geometry Seminar
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Higher category extensions of holonomy mapsfor hyperplane arrangements2017

    • Author(s)
      Toshitake Kohno
    • Organizer
      Arrangements and beyond: Combinatorics, geometry, topology and applications
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Representations of the category of braid cobordisms2017

    • Author(s)
      Toshitake Kohno
    • Organizer
      Self-distributive system and quandle (co)homology theory in algebra and low-dimensional topology
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Higher category extensions of holonomy maps for hyperplane arrangements2016

    • Author(s)
      Toshitake Kohno
    • Organizer
      Summer Conference on Hyperplane Arrangements (SCHA) in Sapporo
    • Place of Presentation
      Hokkaido University
    • Year and Date
      2016-08-08
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Higher category extensions of the holonomy maps of KZ connections2016

    • Author(s)
      Toshitake Kohno
    • Organizer
      Workshop on Grothendieck-Teichmuller Theories
    • Place of Presentation
      Chern Institute of Mathematics, Nankai University, Tianjin, China
    • Year and Date
      2016-07-24
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Holonomy of braids and its 2-category extension2015

    • Author(s)
      T. Kohno
    • Organizer
      Braids, Configuration Spaces and Quantum Topology
    • Place of Presentation
      東京大学
    • Year and Date
      2015-09-07
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Holonomy of braids and its 2-category extension2015

    • Author(s)
      T. Kohno
    • Organizer
      Integrability in Algebra, Geometry and Physics: New Trends
    • Place of Presentation
      Congressi Stefano Franscini, Switzerland
    • Year and Date
      2015-07-13
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Book] 結晶群2015

    • Author(s)
      河野俊丈
    • Total Pages
      200
    • Publisher
      共立出版
    • Related Report
      2015 Research-status Report
  • [Remarks] Toshitake Kohno's Home Page

    • URL

      http://www.ms.u-tokyo.ac.jp/~kohno/

    • Related Report
      2017 Annual Research Report
  • [Remarks] Toshitake Kohno's home page

    • URL

      http://www.ms.u-tokyo.ac.jp/~kohno/

    • Related Report
      2016 Research-status Report
  • [Remarks] Collection of Mathematical Models

    • URL

      http://faculty.ms.u-tokyo.ac.jp/~topology/models/index.html

    • Related Report
      2016 Research-status Report
  • [Remarks]

    • URL

      http://www.ms.u-tokyo.ac.jp/~kohno/

    • Related Report
      2015 Research-status Report
  • [Remarks]

    • URL

      http://www.ms.u-tokyo.ac.jp/teacher/kohno.html

    • Related Report
      2015 Research-status Report
  • [Funded Workshop] Braids, Configuration Spaces and Quantum Topology2015

    • Place of Presentation
      東京大学大学院数理科学研究科大講義室
    • Year and Date
      2015-09-07
    • Related Report
      2015 Research-status Report

URL: 

Published: 2015-04-16   Modified: 2023-03-16  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi