石川 勝巳

Last Update: 2021/06/07 12:54:56

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Name(Kanji/Kana/Abecedarium Latinum)
石川 勝巳/イシカワ カツミ/Ishikawa, Katsumi
Primary Affiliation(Org1/Job title)
Research Institute for Mathematical Sciences (RIMS)/Assistant Professor
Affiliated programs (koza)
Org1 Job title
Graduate School of Science Assistant Professor
E-mail Address
E-mail address
katsumi @ kurims.kyoto-u.ac.jp
Academic Degree
Field(Japanese) Field(English) University(Japanese) University(English) Method
修士(理学) 京都大学 Kyoto University
博士(理学) 京都大学 Kyoto University
Academic Resume (Graduate Schools)
University(Japanese) University(English) Faculty(Japanese) Faculty(English) Major(Japanese) Major(English) Completion Status
京都大学 Kyoto University 大学院理学研究科修士課程数学・数理解析専攻 Graduate School of Science Mathematics and Mathematical Sciences 修了
京都大学 Kyoto University 大学院理学研究科博士後期課程数学・数理解析専攻 Graduate School of Science Mathematics and Mathematical Sciences 修了
Academic Resume (Undergraduate School/Majors)
University(Japanese) University(English) Faculty(Japanese) Faculty(English) Major(s)(Japanese) Major(s)(English) Completion Status
京都大学 Kyoto University 理学部理学科 Faculty of Science 卒業
High School
Highschool Kana
大阪府立岸和田高等学校
Work Experience
Period Organization(Japanese) Organization(English) Job title(Japanese) Job title(English)
2016/04/01-2019/03/31 日本学術振興会 特別研究員 DC1
2019/04/01- 京都大学数理解析研究所 助教
Personal Profile
(Japanese)
低次元トポロジーについて研究している。一般に数学の研究はそれが複雑化・細分化されるにつれ、研究者でなければ何をしているのかすらもわからないといった状態に陥りがちであるが、低次元トポロジーで扱う結び目や3次元多様体といった対象は「見える」という意味で比較的単純で馴染みやすいものであるといえる。このような単純に見えるところに複雑で深い理論が眠っているというのがこの分野の面白いところの1つであり、それを広く伝えられるような研究をしていきたい。
(English)
The main theme of my research is low-dimensional topology, where we study quite ``simple'' objects, such as knots and three manifolds, in the sense that we can recognize them in graphical ways. In contrast to such simpleness it contains a deep theory, and this is an attractive point of low-dimensional topology.
researchmap URL
https://researchmap.jp/katsumin
Research Topics
(Japanese)
低次元トポロジー。特に、結び目や3次元多様体やその不変量についての研究。
(English)
Low-dimensional topology; especially, knots, three-dimensional manifolds, and their invariants.
Overview of the research
(Japanese)
結び目や3次元多様体など、低次元トポロジーの対象について、種々の不変量を用いた研究や、それら不変量そのものについての研究を行っている。特にカンドルと呼ばれる代数系を用いた不変量について研究を行ってきたが、これからはこうした理論を拡張することで古典的な群の理論に収まらない不変量を探すことが重要であると考えている。また最近は結び目の有限型不変量と可逆性の関係についても興味を持って研究を進めている。
(English)
I am interested in various topics in low-dimensional topology including knots, three-dimensional manifolds, and their invariants. In particular, I have studied invariants obtained from quandles, and in my opinion, now it is important to seek new invariants which cannot be obtained in classical group theory by extending quandle theory. Recently, I am also interested in finite type invariants and invertibility of knots.
Fields of research (key words)
Key words(Japanese) Key words(English)
低次元トポロジー Low-dimensional Topology
結び目理論 Knot Theory
Published Papers
Author Author(Japanese) Author(English) Title Title(Japanese) Title(English) Bibliography Bibliography(Japanese) Bibliography(English) Publication date Refereed paper Language Publishing type Disclose
Kazuhiro Ichihara, Katsumi Ishikawa, Eri Matsudo 市原 一裕, 石川 勝巳, 松土 恵理 Kazuhiro Ichihara, Katsumi Ishikawa, Eri Matsudo Minimal coloring numbers on minimal diagrams of torus links Minimal coloring numbers on minimal diagrams of torus links Minimal coloring numbers on minimal diagrams of torus links Journal of Knot Theory and Its Ramifications, 29, 08, 2050059-2050059 , 29, 08, 2050059-2050059 Journal of Knot Theory and Its Ramifications, 29, 08, 2050059-2050059 2020/07 Refereed English Research paper(scientific journal) Disclose to all
Katsumi Ishikawa 石川 勝巳 Katsumi Ishikawa Knot quandles vs. knot biquandles Knot quandles vs. knot biquandles Knot quandles vs. knot biquandles International Journal of Mathematics, 31, 02, 2050015-2050015 , 31, 02, 2050015-2050015 International Journal of Mathematics, 31, 02, 2050015-2050015 2020/02 Refereed English Research paper(scientific journal) Disclose to all
Hirasawa Mikami, Ishikawa Katsumi, Suzuki Masaaki 平澤 美可三, 石川 勝巳, 鈴木 正明 Hirasawa Mikami, Ishikawa Katsumi, Suzuki Masaaki Alternating knots with polynomials having unexpected zeros Alternating knots with polynomials having unexpected zeros Alternating knots with polynomials having unexpected zeros Topology Appl., 253, 48-56 Topology Appl., 253, 48-56 Topology Appl., 253, 48-56 2019/02 Refereed English Disclose to all
Ishikawa Katsumi 石川 勝巳 Ishikawa Katsumi Hoste's conjecture for the 2-bridge knots Hoste's conjecture for the 2-bridge knots Hoste's conjecture for the 2-bridge knots Proc. Amer. Math. Soc., 147, 2245-2254 Proc. Amer. Math. Soc., 147, 2245-2254 Proc. Amer. Math. Soc., 147, 2245-2254 2019/01 Refereed English Disclose to all
Ishikawa Katsumi 石川 勝巳 Ishikawa Katsumi Quandle coloring conditions and zeros of the Alexander polynomials of Montesinos links Quandle coloring conditions and zeros of the Alexander polynomials of Montesinos links Quandle coloring conditions and zeros of the Alexander polynomials of Montesinos links J. Knot Theory Ramifications, 27, 14 J. Knot Theory Ramifications, 27, 14 J. Knot Theory Ramifications, 27, 14 2018/11 Refereed English Disclose to all
Title language:
Conference Activities & Talks
Title Title(Japanese) Title(English) Conference Conference(Japanese) Conference(English) Promotor Promotor(Japanese) Promotor(English) Date Language Assortment Disclose
Generalizations of Galkin quandles and lifting properties of colorings[Invited] Generalizations of Galkin quandles and lifting properties of colorings [Invited] Generalizations of Galkin quandles and lifting properties of colorings [Invited] ハンドル体結び目とその周辺 14 ハンドル体結び目とその周辺 14 2021/06/27 English Disclose to all
Generalizations of Galkin quandles and covering invariants of knots[Invited] Generalizations of Galkin quandles and covering invariants of knots [Invited] Generalizations of Galkin quandles and covering invariants of knots [Invited] The 6th KTGU Mathematics Workshop for Young Researchers The 6th KTGU Mathematics Workshop for Young Researchers The 6th KTGU Mathematics Workshop for Young Researchers 2021/02/16 English Disclose to all
Surjective quandle colorings[Invited] Surjective quandle colorings [Invited] Surjective quandle colorings [Invited] Friday Seminar on Knot Theory Friday Seminar on Knot Theory Friday Seminar on Knot Theory 2020/12/04 English Disclose to all
カンドル彩色で見る結び目理論[Invited] カンドル彩色で見る結び目理論 [Invited] N-KOOKセミナー N-KOOKセミナー 2020/10/24 Japanese Disclose to all
Vanishing of open Jacobi diagrams with odd legs Vanishing of open Jacobi diagrams with odd legs Vanishing of open Jacobi diagrams with odd legs The 15th East Asian Conference on Geometric Topology The 15th East Asian Conference on Geometric Topology The 15th East Asian Conference on Geometric Topology 2020/02/11 English Oral presentation(general) Disclose to all
Vanishing of open Jacobi diagrams with odd legs[Invited] Vanishing of open Jacobi diagrams with odd legs [Invited] Vanishing of open Jacobi diagrams with odd legs [Invited] トポロジー金曜セミナー(九州大学) トポロジー金曜セミナー(九州大学) 2019/07/05 English Public discourse, seminar, tutorial, course, lecture and others Disclose to all
Vanishing of open Jacobi diagrams with odd legs[Invited] Vanishing of open Jacobi diagrams with odd legs [Invited] Vanishing of open Jacobi diagrams with odd legs [Invited] 談話会(京都大学数理解析研究所) 談話会(京都大学数理解析研究所) 2019/06/05 English Public discourse, seminar, tutorial, course, lecture and others Disclose to all
Vanishing of open Jacobi diagrams with odd legs[Invited] Vanishing of open Jacobi diagrams with odd legs [Invited] Vanishing of open Jacobi diagrams with odd legs [Invited] 微分トポロジーセミナー(京都大学数学教室) 微分トポロジーセミナー(京都大学数学教室) 2019/04/16 English Public discourse, seminar, tutorial, course, lecture and others Disclose to all
Quandle coloring conditions and zeros of the Alexander polynomials of Montesinos links[Invited] Quandle coloring conditions and zeros of the Alexander polynomials of Montesinos links [Invited] Quandle coloring conditions and zeros of the Alexander polynomials of Montesinos links [Invited] Kyoto Young Topologists Seminar Kyoto Young Topologists Seminar Kyoto Young Topologists Seminar 2019/02/13 English Oral presentation(general) Disclose to all
On the orbit decomposition of smooth quandles[Invited] On the orbit decomposition of smooth quandles [Invited] On the orbit decomposition of smooth quandles [Invited] カンドルと対称空間 カンドルと対称空間 2018/11/17 English Oral presentation(general) Disclose to all
On zeros of the Alexander polynomials of alternating knots[Invited] On zeros of the Alexander polynomials of alternating knots [Invited] On zeros of the Alexander polynomials of alternating knots [Invited] Topology and Geometry of Low-dimensional Manifolds Topology and Geometry of Low-dimensional Manifolds Topology and Geometry of Low-dimensional Manifolds 2018/10/29 English Oral presentation(general) Disclose to all
Smooth quandleの局所構造とその変形[Invited] Smooth quandleの局所構造とその変形 [Invited] 第65回トポロジーシンポジウム 第65回トポロジーシンポジウム 2018/08/20 Japanese Oral presentation(general) Disclose to all
On the fundamental ``quandle'' of a handlebody-knot[Invited] On the fundamental ``quandle'' of a handlebody-knot [Invited] On the fundamental ``quandle'' of a handlebody-knot [Invited] Tsuda-Gakugei Topology Workshop Tsuda-Gakugei Topology Workshop Tsuda-Gakugei Topology Workshop 2018/07/30 English Oral presentation(general) Disclose to all
A link-homotopy invariant for surface links[Invited] A link-homotopy invariant for surface links [Invited] A link-homotopy invariant for surface links [Invited] Friday Seminar on Knot Theory Friday Seminar on Knot Theory Friday Seminar on Knot Theory 2018/06/29 English Public discourse, seminar, tutorial, course, lecture and others Disclose to all
A link-homotopy invariant for surface links[Invited] A link-homotopy invariant for surface links [Invited] A link-homotopy invariant for surface links [Invited] Low dimensional topology and number theory X Low dimensional topology and number theory X Low dimensional topology and number theory X 2018/03/29 English Oral presentation(general) Disclose to all
A quandle approach to Hoste's conjecture[Invited] A quandle approach to Hoste's conjecture [Invited] A quandle approach to Hoste's conjecture [Invited] Branched Coverings, Degenerations, and Related Topics 2018 Branched Coverings, Degenerations, and Related Topics 2018 Branched Coverings, Degenerations, and Related Topics 2018 2018/03/06 English Oral presentation(general) Disclose to all
A relation between biquandle colorings and quandle colorings A relation between biquandle colorings and quandle colorings A relation between biquandle colorings and quandle colorings 結び目の数学X 結び目の数学X 2017/12/26 English Oral presentation(general) Disclose to all
A relation between biquandle coloring and quandle coloring[Invited] A relation between biquandle coloring and quandle coloring [Invited] A relation between biquandle coloring and quandle coloring [Invited] 筑波大学トポロジーセミナー 筑波大学トポロジーセミナー 2017/09/21 English Public discourse, seminar, tutorial, course, lecture and others Disclose to all
Hoste's conjecture for the Alexander polynomials of the 2-bridge knots Hoste's conjecture for the Alexander polynomials of the 2-bridge knots Hoste's conjecture for the Alexander polynomials of the 2-bridge knots 拡大KOOKセミナー2017 拡大KOOKセミナー2017 2017/08/28 English Oral presentation(general) Disclose to all
The automorphism group of a smooth quandle The automorphism group of a smooth quandle The automorphism group of a smooth quandle The 12th East Asian School of Knots and Related Topics The 12th East Asian School of Knots and Related Topics The 12th East Asian School of Knots and Related Topics 2017/02/14 English Oral presentation(general) Disclose to all
smooth quandleの自己同型群[Invited] smooth quandleの自己同型群 [Invited] トポロジー金曜セミナー(九州大学) トポロジー金曜セミナー(九州大学) 2017/01/20 Japanese Public discourse, seminar, tutorial, course, lecture and others Disclose to all
On the classification of smooth quandles[Invited] On the classification of smooth quandles [Invited] On the classification of smooth quandles [Invited] Friday Seminar on Knot Theory Friday Seminar on Knot Theory Friday Seminar on Knot Theory 2016/10/28 English Public discourse, seminar, tutorial, course, lecture and others Disclose to all
Smooth quandle structures on closed surfaces Smooth quandle structures on closed surfaces Smooth quandle structures on closed surfaces The 8th KOOK-TAPU Joint Seminar on Knots and Related Topics & The 10th Graduate Student Workshop on Mathematics The 8th KOOK-TAPU Joint Seminar on Knots and Related Topics & The 10th Graduate Student Workshop on Mathematics The 8th KOOK-TAPU Joint Seminar on Knots and Related Topics & The 10th Graduate Student Workshop on Mathematics 2016/07/28 English Oral presentation(general) Disclose to all
Smooth quandle structures on closed surfaces[Invited] Smooth quandle structures on closed surfaces [Invited] Smooth quandle structures on closed surfaces [Invited] 微分トポロジーセミナー(京都大学数学教室) 微分トポロジーセミナー(京都大学数学教室) 2016/06/07 Japanese Public discourse, seminar, tutorial, course, lecture and others Disclose to all
Quandle cocycle invariants of cabled surface knots[Invited] Quandle cocycle invariants of cabled surface knots [Invited] Quandle cocycle invariants of cabled surface knots [Invited] Intelligence of Low-dimensional Topology Intelligence of Low-dimensional Topology Intelligence of Low-dimensional Topology 2016/05/20 English Oral presentation(general) Disclose to all
Cabling formulae of quandle cocycle invariants for surface knots Cabling formulae of quandle cocycle invariants for surface knots Cabling formulae of quandle cocycle invariants for surface knots 結び目の数学VIII 結び目の数学VIII 2015/12/25 English Oral presentation(general) Disclose to all

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Title language:
External funds: competitive funds and Grants-in-Aid for Scientific Research (Kakenhi)
Type Position Title(Japanese) Title(English) Period
若手研究 Representative Kontsevich不変量と結び目の可逆性 (2020年度分) 2020/04/01-2021/03/31
Teaching subject(s)
Name(Japanese) Name(English) Term Department Period
現代の数学と数理解析-基礎概念とその諸科学への広がり Invitation to Modern Mathematics and Mathematical Sciences - Basic concepts and their role in various sciences 前期 全学共通科目 2020/04-2021/03
現代の数学と数理解析-基礎概念とその諸科学への広がり Invitation to Modern Mathematics and Mathematical Sciences - Basic concepts and their role in various sciences 前期 全学共通科目 2021/04-2022/03