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Organized research on computational complexity via algebraic geometry

Research Project

Project/Area Number 17K19954
Research Category

Grant-in-Aid for Challenging Research (Exploratory)

Allocation TypeMulti-year Fund
Research Field Information science, computer engineering, and related fields
Research InstitutionKwansei Gakuin University (2019-2020)
Tohoku University (2017-2018)

Principal Investigator

Tokuyama Takeshi  関西学院大学, 理工学部, 教授 (40312631)

Project Period (FY) 2017-06-30 – 2021-03-31
Project Status Completed (Fiscal Year 2020)
Budget Amount *help
¥6,370,000 (Direct Cost: ¥4,900,000、Indirect Cost: ¥1,470,000)
Fiscal Year 2019: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2018: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords計算理論 / 代数幾何学 / 群の表現論 / 計算複雑度 / 表現論 / 計算幾何学 / 計算階層
Outline of Final Research Achievements

Our grand challenge is the integration of mathematics and theory of computing. In particular, we aim at construction of collaborating research between researchers of mathematics (mainly algebraic geometry and group representation theory) and theory of computing, and pursue joint study focusing on GCT (Geometric Complexity Theory). We organized bi-monthly seminar held at Komaba campus of University of Tokyo. Moreover, we promoted international joint study, and participated to a joint seminar at Max Plank Institute in Germany, where Tokuyama and three other Japanese joint researchers gave invited talks. We also invited Prof. Ikenmeyer (U. Liverpool, UK) and Mr. Fisher (PhD student) to have joint study and series of lectures in Sendai, Kyoto, and Tokyo.

Academic Significance and Societal Importance of the Research Achievements

本研究では、数学と情報科学分野の研究連携の推進を目指し、代数幾何学と群の表現論を計算複雑度解明に活用するGCTを中心とした、組織的な研究を行った。トップレベル研究者による定例セミナーと国際的な先端研究者や研究機関との国際共同研究を実施し、新しい成果を得た。一例として、一般化行列式を用いたWeylの公式の拡張は、数学的に基本的な公式の拡張であるのみならず、統計物理学や量子計算等の多くの分野への波及が期待される。また、数学と情報科学分野の連携に関して広く活動し、JST俯瞰セミナー等数多くの意義の高い啓蒙を行った。

Report

(5 results)
  • 2020 Annual Research Report   Final Research Report ( PDF )
  • 2019 Research-status Report
  • 2018 Research-status Report
  • 2017 Research-status Report
  • Research Products

    (25 results)

All 2020 2019 2018 2017 Other

All Int'l Joint Research (11 results) Journal Article (6 results) (of which Int'l Joint Research: 3 results,  Peer Reviewed: 6 results,  Open Access: 4 results) Presentation (7 results) (of which Int'l Joint Research: 2 results,  Invited: 6 results) Book (1 results)

  • [Int'l Joint Research] タフツ大学(米国)

    • Related Report
      2020 Annual Research Report
  • [Int'l Joint Research] ベルリン自由大学(ドイツ)

    • Related Report
      2020 Annual Research Report
  • [Int'l Joint Research] Universita della Svizzera Italiana(イタリア)

    • Related Report
      2020 Annual Research Report
  • [Int'l Joint Research] Max Plank Institute fur Informatics(ドイツ)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] University of Liverpool(英国)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] POSTECH(韓国)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] Max Plank Institute for Informatics(ドイツ)

    • Related Report
      2018 Research-status Report
  • [Int'l Joint Research] MPII/ベルリン自由大学(ドイツ)

    • Related Report
      2017 Research-status Report
  • [Int'l Joint Research] Lund大学(スウェーデン)

    • Related Report
      2017 Research-status Report
  • [Int'l Joint Research] Eindhoven大学/Utrecht大学(オランダ)

    • Related Report
      2017 Research-status Report
  • [Int'l Joint Research] カタルニア工科大学(スペイン)

    • Related Report
      2017 Research-status Report
  • [Journal Article] Distance Bounds for High Dimensional Consistent Digital Rays and 2-D Partially-Consistent Digital Rays2020

    • Author(s)
      Man-Kwun Chiu, Matias Korman, Martin Suderland, Takeshi Tokuyama
    • Journal Title

      Proc. ESA 2020

      Volume: 1

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Consistent Digital Curved Rays and Pseudoline Arrangements2019

    • Author(s)
      Jinhee Chun, Kenya Kikuchi, Takeshi Tokuyama
    • Journal Title

      27th Annual European Symposium on Algorithms

      Volume: 27

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Capsule Net for Micro-Expression Recognition2019

    • Author(s)
      Nguyen Van Quang, Jinhee Chun, Takeshi Tokuyama
    • Journal Title

      The 14th IEEE International Conference on Automatic Face and Gesture Recognition(FG 2019)

      Volume: 2019 Pages: 1-7

    • DOI

      10.1109/fg.2019.8756544

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Model-Agnostic Explanations for Decisions Using Minimal Patterns2019

    • Author(s)
      Kohei Asano, Jinhee Chun, Atsushi Koike, Takeshi Tokuyama
    • Journal Title

      The 28th International Conference on Artificial Neural Networks

      Volume: LNCS11727 Pages: 241-252

    • DOI

      10.1007/978-3-030-30487-4_19

    • ISBN
      9783030304867, 9783030304874
    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Colored spanning graphs for set visualization2018

    • Author(s)
      Hurtado Ferran、Korman Matias、van Kreveld Marc、Loffler Maarten、Sacristan Vera、Shioura Akiyoshi、Silveira Rodrigo I.、Speckmann Bettina、Tokuyama Takeshi
    • Journal Title

      Computational Geometry: Theory and Applications

      Volume: 68 Pages: 262-276

    • DOI

      10.1016/j.comgeo.2017.06.006

    • Related Report
      2018 Research-status Report 2017 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Efficiently Correcting Matrix Products2017

    • Author(s)
      Gasieniec Leszek、Levcopoulos Christos、Lingas Andrzej、Pagh Rasmus、Tokuyama Takeshi
    • Journal Title

      Algorithmica

      Volume: 79 Issue: 2 Pages: 428-443

    • DOI

      10.1007/s00453-016-0202-3

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Presentation] 数学の広がり2020

    • Author(s)
      徳山 豪
    • Organizer
      JST-CDRS 俯瞰ワークショップ 数学と科学、工学の協働に関する連続セミナー
    • Related Report
      2020 Annual Research Report
    • Invited
  • [Presentation] Does Alice confuse Geometric Complexity Theory? Dodgson's Condensation Algorithm and Related Topics2020

    • Author(s)
      Takeshi Tokuyama
    • Organizer
      Kyoto University Informatics Seminar
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] Near-unit distance embedding of points in the plane and space2019

    • Author(s)
      Tetsuo Asano, Naoki Katoh, Takeshi Tokuyama
    • Organizer
      WAAC 2019
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] A q-Determinant Formula for Deformation of Weyl Character Formula2019

    • Author(s)
      Takeshi Tokuyama
    • Organizer
      POSTECH Algorithm Research Workshop
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] 行列式の一般化とアルゴリズムや数理2019

    • Author(s)
      徳山 豪
    • Organizer
      南大阪 代数セミナー
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] Deformation of Determinants and Related Combinatorics and Computation2019

    • Author(s)
      Takeshi Tokuyama
    • Organizer
      MPI-INF and MPI-MiS joint workshop on Theoretical Computer Science and Algebraic Geometry
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 計算複雑度と数学との接点について2017

    • Author(s)
      徳山 豪
    • Organizer
      表現論シンポジウム 2017
    • Related Report
      2017 Research-status Report
    • Invited
  • [Book] Beyod Planara Graphs2020

    • Author(s)
      Seokhee Hong, Takeshi Tokuyama (eds)
    • Total Pages
      270
    • Publisher
      Springer Verlag
    • ISBN
      9789811565328
    • Related Report
      2020 Annual Research Report

URL: 

Published: 2017-07-21   Modified: 2022-01-27  

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