Computational methods in equivariant topology with applications in discrete problems

• Project/Area Number: 26800043
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Yamaguchi University
• Principal Investigator: KAJI Shizuo 山口大学, 大学院創成科学研究科, 准教授 (00509656)
• Research Collaborator: Choi Suyoung Ajou University, Associate Professor ; Theriault Stephen Southampton University, Professor
• Project Period (FY): 2014-04-01 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000); Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
• Keywords: 位相幾何学 / 同変トポロジー / 旗多様体 / トーリック多様体 / トポロジー / ホモトピー分解 / H空間 / スティーンロッド代数 / コホモロジー / グラフィックス / リー群 / 同変コホモロジー / シューベルトカルキュラス

Outline of Final Research Achievements

Spaces with nice group actions, such as flag manifolds and toric manifolds, are studied by algebraic topological and combinatorial techniques. Algorithms to deal with cohomology rings and cohomology operations are obtained and implemented.

Research Products

• [Int'l Joint Research] Ajou University/KIAS(韓国)
• [Int'l Joint Research] Southampton University(英国)
• [Int'l Joint Research] サウサンプトン大学(英国)
• [Int'l Joint Research] ハイデルベルグ大学(ドイツ)
• [Int'l Joint Research] 東地中海大学(キプロス)
• [Int'l Joint Research] アジョウ大学(韓国)
• [Int'l Joint Research] Southampton university(英国)
• [Int'l Joint Research] Ajou university(韓国)
• [Int'l Joint Research] Heidelberg university(ドイツ)
• [Journal Article] The mod 2 dual Steenrod algebra as a subalgebra of the mod 2 dual Leibniz-Hopf algebra (2017)
  • Author(s): N. D. Turgay and S. Kaji
  • Journal Title: Journal of Homotopy and Related Structures Volume: 印刷中 Issue: 3 Pages: 727-739
  • DOI: 10.1007/s40062-016-0163-x
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Homotopy decomposition of a suspended real toric space (2017)
  • Author(s): S. Choi, S. Kaji, and S. Theriault
  • Journal Title: the Boletin de la Sociedad Matematica Mexicana Volume: 23 Issue: 1 Pages: 153-161
  • DOI: 10.1007/s40590-016-0090-1
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Counting the number of homotopy associative multiplications on certain H-spaces (2016)
  • Author(s): Shizuo Kaji, Michihiro Sakai, Stephen Theriault
  • Journal Title: Topology and its Applications Volume: 214 Pages: 137-149
  • DOI: 10.1016/j.topol.2016.10.008
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Three presentations of torus equivariant cohomology of flag manifolds (2016)
  • Author(s): Shizuo Kaji
  • Journal Title: Proceedings of International Mathematics Conference in honour of the 70th Birthday of Professor S. A. Ilori Volume: NA
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Tetrisation of triangular meshes and its application in shape blending (2016)
  • Author(s): S. Kaji
  • Journal Title: Mathematical Progress in Expressive Image Synthesis Volume: III
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Mod p decompositions of the loop spaces of compact symmetric spaces (2015)
  • Author(s): Shizuo KAJI, Akihiro Ohsita, and Stephen Theriault
  • Journal Title: Algebraic & Geometric Topology Volume: 15 Issue: 3 Pages: 1771-1811
  • DOI: 10.2140/agt.2015.15.1771
  • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Three presentations of torus equivariant cohomology of flag manifolds (2015)
  • Author(s): S. Kaji
  • Journal Title: Proceedings of International Mathematics Conference in honour of the 70th Birthday of Professor S. A. Ilori Volume: 印刷中
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Probe-type deformers (2014)
  • Author(s): S. Kaji and G. Liu
  • Journal Title: MI Lecture Notes Volume: 58 Pages: 26-35
  • Peer Reviewed
• [Presentation] Point and diagonal classes in flag varieties (2017)
  • Author(s): S. Kaji
  • Organizer: The 7th East Asian Conference on Algebraic Topology (EACAT 2017)
  • Int'l Joint Research
• [Presentation] A secondary and equivariant string product (2017)
  • Author(s): S. Kaji
  • Organizer: Young Researchers in Homotopy theory and Toric topology 2017
  • Int'l Joint Research
• [Presentation] Representations on Real Toric Manifolds (2017)
  • Author(s): S. Kaji
  • Organizer: Princeton-Rider workshop on the Homotopy Theory of Polyhedral Products
  • Int'l Joint Research
• [Presentation] A type-A Weyl group action on the associated real toric manifold (2016)
  • Author(s): S. Kaji
  • Organizer: The 4th Korea Toric Topology Workshop
  • Place of Presentation: Jeju University, Jeju (Korea)
  • Year and Date: 2016-12-27
  • Int'l Joint Research / Invited
• [Presentation] Equivariant string products (2016)
  • Author(s): S. Kaji
  • Organizer: The 5th GeToPhyMa: Summer school "Rational homotopy theory and its interactions" celebrating Jim Stasheff and Dennis Sullivan for their 80th and 75 anniversary
  • Place of Presentation: UIR Rabat, Rabat (Morocco)
  • Year and Date: 2016-07-20
  • Int'l Joint Research
• [Presentation] Homotopy decomposition of a suspended real toric space (2016)
  • Author(s): S. Kaji
  • Organizer: Toric Topology 2016 in Kagoshima
  • Place of Presentation: 鹿児島大学(鹿児島県鹿児島市)
  • Year and Date: 2016-04-20
  • Int'l Joint Research
• [Presentation] Products in equivariant homology (2015)
  • Author(s): S. Kaji
  • Organizer: The 3rd Korea Toric Topology Winter Workshop
  • Place of Presentation: The-K Hotel, Gyeongju, Korea
  • Year and Date: 2015-12-29
  • Int'l Joint Research / Invited
• [Presentation] Tetrisation of triangular meshes and its application in shape blending (2015)
  • Author(s): S. Kaji
  • Organizer: MEIS2015
  • Place of Presentation: Nishijin plaza, Kyushu university (福岡県福岡市)
  • Year and Date: 2015-09-26
  • Int'l Joint Research
• [Presentation] The dual Steenrod algebra and the overlapping shuffle product (2015)
  • Author(s): S. Kaji
  • Organizer: Antalya Algebra Days XVII
  • Place of Presentation: Nesin Maths Village, Turkey
  • Year and Date: 2015-05-23
  • Int'l Joint Research
• [Presentation] Homotopy decomposition of a suspended flag manifold (2015)
  • Author(s): S. Kaji
  • Organizer: IMPANGA15
  • Place of Presentation: Banach center at Bedlewo, Poland
  • Year and Date: 2015-04-13
  • Int'l Joint Research
• [Presentation] External products in equivariant homology (2015)
  • Author(s): S. Kaji
  • Organizer: Torus Actions in Geometry, Topology, and Applications
  • Place of Presentation: Skoltech, Moscow、ロシア
  • Year and Date: 2015-02-17
  • Invited
• [Presentation] Mod p decompositions of the loop spaces of flag manifolds (2015)
  • Author(s): S. Kaji
  • Organizer: International Mathematics Conference, in honour of the 70th Birthday of Professor S. A. Ilori
  • Place of Presentation: Ibadan大学, ナイジェリア
  • Year and Date: 2015-01-12
  • Invited
• [Presentation] Shape deformation in Computer graphics (2014)
  • Author(s): S. Kaji
  • Organizer: Discrete, Computational and Algebraic Topology
  • Place of Presentation: コペンハーゲン大学, デンマーク
  • Year and Date: 2014-11-10 – 2014-11-14
• [Presentation] Mod-p decompositions of the loop spaces of compact symmetric spaces (2014)
  • Author(s): S. Kaji
  • Organizer: 29th British Topology Meeting
  • Place of Presentation: サウサンプトン大学, 英国
  • Year and Date: 2014-09-08
• [Remarks] Shizuo KAJI's homepage
  • URL: http://www.skaji.org
• [Remarks] 研究者ホームページ
  • URL: https://skaji.org
• [Remarks] github プログラム公開場所
  • URL: https://github.com/shizuo-kaji
• [Remarks] Shizuo KAJI's homepage
  • URL: http://www.skaji.org/home/publications
• [Remarks] Shizuo KAJI's homepage
  • URL: http://skaji.org