ISHII Atsushi
- Affiliation
- Institute of Pure and Applied Sciences
- Official title
- Associate Professor
- URL
- Research fields
Geometry - Research keywords
low-dimensional topology - Research projects
Geometry of handlebody-knots 2021-04 -- 2026-03 ISHII Atsushi Japan Society for the Promotion of Science/Grant-in-Aid for Scientific Research (C) 3,900,000Yen Handlebody-knots and augmented Alexander invariants 2018-04 -- 2022-03 ISHII Atsushi Japan Society for the Promotion of Science/Grant-in-Aid for Scientific Research (C) 4,290,000Yen Orientations and invariants of handlebody-knots 2015-04 -- 2018-03 ISHII Atsushi Japan Society for the Promotion of Science/Grant-in-Aid for Scientific Research (C) 4,680,000Yen Handlebody-knots and invariants 2012-04 -- 2015-03 ISHII Atsushi Japan Society for the Promotion of Science/Grant-in-Aid for Young Scientists (B) 4,420,000Yen Handlebody-knots and topology 2009 -- 2012-03 ISHII Atsushi Japan Society for the Promotion of Science/Grant-in-Aid for Young Scientists (B) 4,030,000Yen - Career history
2005-04 -- 2007-03 JSPSOsaka UniversityResearch Fellow 2007-04 -- 2008-08 JSPSRIMS, Kyoto UniversityResearch Fellow 2008-09 -- 2013-04 (University of Tsukuba)大学院数理物質科学研究科Assistant Professor 2013-05 -- 2019-11 (University of Tsukuba)数理物質系（数学域）講師 2019-12 -- (current) (University of Tsukuba)数理物質系（数学域）准教授 - Degree
2006-03 博士(理学) Osaka University - Academic societies
2003-04 -- (current) The Mathematical Society of Japan -- (current) The Mathematical Society of Japan -- (current) The Mathematical Society of Japan - Articles
- Shade quandle presentations for oriented links
Ishii Atsushi; Kawamura Kengo; Oshiro Kanako; Taniguch...
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS/34(01), 2025-01 - Normalized quandle twisted Alexander invariants
Ishii Atsushi; Oshiro Kanako
INTERNATIONAL JOURNAL OF MATHEMATICS/35(05), 2024-04 - QUANDLE TWISTED ALEXANDER INVARIANTS
Ishii Atsushi; Oshiro Kanako
OSAKA JOURNAL OF MATHEMATICS/59(3)/pp.683-702, 2022-06 - Derivatives with Alexander pairs for quandles
Ishii Atsushi; Oshiro Kanako
FUNDAMENTA MATHEMATICAE/259(1)/pp.1-31 - The fundamental multiple conjugation quandle of a handlebody-link
Ishii Atsushi
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN/74(1)/pp.1-23, 2022-01 - Cocycles of G-Alexander biquandles and G-Alexander multiple conjugation biquandles
Ishii Atsushi; Iwakiri Masahide; Kamada Seiichi; Kim Jie...
TOPOLOGY AND ITS APPLICATIONS/301(SI), 2021-09 - Row relations of twisted Alexander matrices and shadow quandle 2-cocycles
Ishii Atsushi; Oshiro Kanako
TOPOLOGY AND ITS APPLICATIONS/301(SI), 2021-09 - Handlebody-knots and the development of quandle theory
石井 敦
SUGAKU/70(1)/pp.63-80, 2018 - A multiple group rack and oriented spatial surfaces
Ishii Atsushi; Matsuzaki Shosaku; Murao Tomo
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS/29(7), 2020-06 - Biquandle (co)homology and handlebody-links
Ishii Atsushi; Iwakiri Masahide; Kamada Seiichi; Kim Jie...
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS/27(11:::SI), 2018-10 - ON CALCULATIONS OF THE TWISTED ALEXANDER IDEALS FOR SPATIAL GRAPHS, HANDLEBODY-KNOTS AND SURFACE-LINKS
Ishii Atsushi; Nikkuni Ryo; Oshiro Kanako
OSAKA JOURNAL OF MATHEMATICS/55(2)/pp.297-313, 2018-04 - A multiple conjugation biquandle and handlebody-links
Ishii Atsushi; Iwakiri Masahide; Kamada Seiichi; Kim Jie...
HIROSHIMA MATHEMATICAL JOURNAL/48(1)/pp.89-117, 2018-03 - HOMOLOGY FOR QUANDLES WITH PARTIAL GROUP OPERATIONS
Carter Scott; Ishii Atsushi; Saito Masahico; Tanaka Kokoro
PACIFIC JOURNAL OF MATHEMATICS/287(1)/pp.19-48, 2017-03 - The Markov theorems for spatial graphs and handlebody-knots with Y-orientations
Ishii Atsushi
INTERNATIONAL JOURNAL OF MATHEMATICS/26(14), 2015-12 - A multiple conjugation quandle and handlebody-knots
Ishii Atsushi
TOPOLOGY AND ITS APPLICATIONS/196(B)/pp.492-500, 2015-12 - Handlebody-knot invariants derived from unimodular Hopf algebras
Masuoka Akira; Ishii Atsushi
Journal of Knot Theory and its Ramifications/23(7)/p.1460001, 2014-06 - Handlebody-knot invariants derived from unimodular Hopf algebras
Ishii Atsushi
J. Knot Theory Ramifications/23/p.1460001, 2014 - A G-family of quandles and handlebody-knots
Ishii Atsushi; Masahide Iwakiri; Yeonhee Jang; Kanako Oshiro
Illinois J. Math./57/pp.817-838, 2013 - Knotted handle decomposing spheres for handlebody-knots
Ishii Atsushi; Kishimoto Kengo; Ozawa Makoto
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN/67(1)/pp.407-417, 2015-01 - The quandle coloring invariant of a reducible handlebody-knot
Ishii Atsushi; Kishimoto Kengo
Tsukuba J. Math. 35 (2011) 131--141./35/pp.131-141, 2011-07 - On normalizations of a regular isotopy invariant for spatial graphs
Ishii Atsushi
INTERNATIONAL JOURNAL OF MATHEMATICS/22(11)/pp.1545-1559, 2011-11 - The Links-Gould invariants of the Kanenobu knots
Atsushi Ishii
Kobe J. Math./20/p.53-61, 2003-01 - The Links-Gould invariant of closed 3-braids
Atsushi Ishii
J. Knot Theory Ramifications/13/p.41-56, 2004-01 - Algebraic links and skein relations of the Links-Gould invariant
Atsushi Ishii
Proc. Amer. Math. Soc./132/p.3741-3749, 2004-01 - Different links with the same Links-Gould invariant
Atsushi Ishii; Taizo Kanenobu
Osaka J. Math./42/p.273-290, 2005-01 - more...
- Shade quandle presentations for oriented links
- Conference, etc.
- Partially multiplicative biquandles and handlebody-knots
Ishii Atsushi; Nelson Sam
AMS Fall Western Sectional Meeting/2015-10-24--2015-10-25
- Partially multiplicative biquandles and handlebody-knots
- Teaching
2024-04 -- 2024-08 Research in Geometry IB University of Tsukuba. 2024-10 -- 2025-02 Research in Geometry IIA University of Tsukuba. 2024-10 -- 2025-02 Research in Geometry IA University of Tsukuba. 2024-04 -- 2024-08 Research in Geometry IIIB University of Tsukuba. 2024-04 -- 2024-08 Seminar on Mathematics University of Tsukuba. 2024-10 -- 2025-02 Seminar on Mathematics University of Tsukuba. 2024-04 -- 2024-08 Geometry I University of Tsukuba. 2024-04 -- 2024-08 Research in Geometry IIIA University of Tsukuba. 2024-10 -- 2025-02 Research in Geometry VA University of Tsukuba. 2024-04 -- 2024-08 Research in Geometry VB University of Tsukuba. more... - Talks
- On bracket polynomials for Alexander-type invariants
石井 敦
金沢トポロジーセミナー/2025-06-12--2025-06-12 - Determinant state sum formulas for Alexander-type invariants
石井 敦
日本数学会年会/2025-03-18--2025-03-21 - A bracket polynomial for the Alexander--Conway polynomial
石井 敦
結び目の数理VII/2024-12-24--2024-12-27 - The Alexander polynomial and the Jones polynomial
石井 敦
数理科学セミナー/2024-10-03--2024-10-03 - On a bracket polynomial for the Alexander--Conway polynomial
石井 敦
Knots and Related Topics/2024-09-11--2024-09-12 - Quandle twisted Alexander invariants with cohomologous Alexander pairs
石井 敦
数理情報科学セミナー/2023-09-28--2023-09-28 - Alexander type invariants of groups, quandles and MCQs
石井 敦
日本数学会年会/2023-03-15--2023-03-18 - On normalization of Alexander type invariants
石井 敦
拡大KOOKセミナー2022/2022-08-30--2022-09-01
- On bracket polynomials for Alexander-type invariants
(Last updated: 2025-07-29)