Basic Information

Affiliated programs (koza)

• Graduate School of Science, 数学・数理解析専攻 数理解析基礎講座, 助教

Academic Degree

• (Kyoto University)
• (Kyoto University)

Academic Resume (Graduate Schools)

• Kyoto University, Graduate School of Science, Mathematics and Mathematical Sciences, 修了
• Kyoto University, Graduate School of Science, Mathematics and Mathematical Sciences, 修了

Academic Resume (Undergraduate School/Majors)

• Kyoto University, Faculty of Science, 卒業

High School

• High School

  大阪府立岸和田高等学校

ID,URL

• J-Global ID

  201901014636797754

researchmap URL

• https://researchmap.jp/katsumin

Research

Research Topics, Overview of the research

• Research Topics

  Low-dimensional topology; especially, knots, three-dimensional manifolds, and their invariants.

• Overview of the research

  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.

Research Areas

• Natural sciences, Geometry

Papers

• Quandle colorings vs. biquandle colorings

  Katsumi Ishikawa; Kokoro Tanaka

  Topology and its Applications, Mar. 2024, Peer-reviewed

  
• Two-tone colorings and surjective dihedral representations for links

  Kazuhiro Ichihara; Katsumi Ishikawa; Eri Matsudo; Masaaki Suzuki

  Osaka Journal of Mathematics (accepted), 23 Apr. 2024, Peer-reviewed

  
• Minimal coloring numbers on minimal diagrams of torus links

  Kazuhiro Ichihara; Katsumi Ishikawa; Eri Matsudo

  Journal of Knot Theory and Its Ramifications, Jul. 2020, Peer-reviewed

  
• Knot quandles vs. knot biquandles

  Katsumi Ishikawa

  International Journal of Mathematics, Feb. 2020, Peer-reviewed

  
• Alternating knots with polynomials having unexpected zeros

  Hirasawa Mikami; Ishikawa Katsumi; Suzuki Masaaki

  Topology Appl., Feb. 2019, Peer-reviewed

  
• Hoste's conjecture for the 2-bridge knots

  Ishikawa Katsumi

  Proc. Amer. Math. Soc., Jan. 2019, Peer-reviewed

  
• Quandle coloring conditions and zeros of the Alexander polynomials of Montesinos links

  Ishikawa Katsumi

  J. Knot Theory Ramifications, Nov. 2018, Peer-reviewed

  

Misc.

• Quandle cocycle invariants of cabled surface knots (Intelligence of Low-dimensional Topology)

  Ishikawa Katsumi

  RIMS Kokyuroku, Jul. 2016

  Access this misc :

  

Presentations

• The trapezoidal conjecture for the links of braid index 3

  石川 勝巳

  東京大学トポロジー火曜セミナー, 04 Jun. 2024, Invited

  
• The trapezoidal conjecture for knots and links of braid index 3

  Katsumi Ishikawa

  Knot theory, LMO invariants and related topics, 09 Mar. 2024, Invited

  
• The trapezoidal conjecture for links of braid index 3

  Katsumi Ishikawa

  The 19th East Asian Conference on Geometric Topology, 19 Feb. 2024, Invited

  
• Twisted Alexander vanishing order

  石川 勝巳

  京都大学微分トポロジーセミナー, 14 Nov. 2023, Invited

  
• Finite groups admitting knot representations with twisted Alexander polynomials zero

  石川 勝巳

  拡大KOOKセミナー 2023, 30 Aug. 2023

  
• Torsions in Jacobi diagram spaces

  石川 勝巳

  結び目の数理 V, 23 Dec. 2022

  
• Extended quandle spaces and their applications

  Katsumi Ishikawa

  広島大学 トポロジー・幾何セミナー, 21 Dec. 2021, Invited

  
• Extended quandle spaces and their applications

  Katsumi Ishikawa

  Quandles and Symmetric Spaces, 26 Nov. 2021, Invited

  
• A spectral sequence on quandle homology

  Katsumi Ishikawa

  Friday Seminar on Knot Theory, 08 Oct. 2021, Invited

  
• On the associated groups of the quandles

  石川 勝巳

  拡大KOOKセミナー 2021, 31 Aug. 2021

  
• Generalizations of Galkin quandles and lifting properties of colorings

  石川 勝巳

  ハンドル体結び目とその周辺 14, 27 Jun. 2021, Invited

  
• Generalizations of Galkin quandles and covering invariants of knots

  石川 勝巳

  The 6th KTGU Mathematics Workshop for Young Researchers, 16 Feb. 2021, Invited

  
• Surjective quandle colorings

  石川 勝巳

  Friday Seminar on Knot Theory, 04 Dec. 2020, Invited

  
• カンドル彩色で見る結び目理論

  石川 勝巳

  N-KOOKセミナー, 24 Oct. 2020, Invited

  
• Vanishing of open Jacobi diagrams with odd legs

  Katsumi Ishikawa

  The 15th East Asian Conference on Geometric Topology, 11 Feb. 2020

  
• Vanishing of open Jacobi diagrams with odd legs

  Ishikawa Katsumi

  トポロジー金曜セミナー（九州大学）, 05 Jul. 2019, Invited

  
• Vanishing of open Jacobi diagrams with odd legs

  Ishikawa Katsumi

  談話会（京都大学数理解析研究所）, 05 Jun. 2019, Invited

  
• Vanishing of open Jacobi diagrams with odd legs

  Ishikawa Katsumi

  微分トポロジーセミナー（京都大学数学教室）, 16 Apr. 2019, Invited

  
• Quandle coloring conditions and zeros of the Alexander polynomials of Montesinos links

  Ishikawa Katsumi

  Kyoto Young Topologists Seminar, 13 Feb. 2019, Invited

  
• On the orbit decomposition of smooth quandles

  Ishikawa Katsumi

  カンドルと対称空間, 17 Nov. 2018, Invited

  
• On zeros of the Alexander polynomials of alternating knots

  Ishikawa Katsumi

  Topology and Geometry of Low-dimensional Manifolds, 29 Oct. 2018, Invited

  
• Smooth quandleの局所構造とその変形

  石川 勝巳

  第65回トポロジーシンポジウム, 20 Aug. 2018, Invited

  
• On the fundamental ``quandle'' of a handlebody-knot

  Ishikawa Katsumi

  Tsuda-Gakugei Topology Workshop, 30 Jul. 2018, Invited

  
• A link-homotopy invariant for surface links

  Ishikawa Katsumi

  Friday Seminar on Knot Theory, 29 Jun. 2018, Invited

  
• A link-homotopy invariant for surface links

  Ishikawa Katsumi

  Low dimensional topology and number theory X, 29 Mar. 2018, Invited

  
• A quandle approach to Hoste's conjecture

  Ishikawa Katsumi

  Branched Coverings, Degenerations, and Related Topics 2018, 06 Mar. 2018, Invited

  
• A relation between biquandle colorings and quandle colorings

  Ishikawa Katsumi

  結び目の数学X, 26 Dec. 2017

  
• A relation between biquandle coloring and quandle coloring

  Ishikawa Katsumi

  筑波大学トポロジーセミナー, 21 Sep. 2017, Invited

  
• Hoste's conjecture for the Alexander polynomials of the 2-bridge knots

  Ishikawa Katsumi

  拡大KOOKセミナー2017, 28 Aug. 2017

  
• The automorphism group of a smooth quandle

  Ishikawa Katsumi

  The 12th East Asian School of Knots and Related Topics, 14 Feb. 2017

  
• smooth quandleの自己同型群

  石川 勝巳

  トポロジー金曜セミナー（九州大学）, 20 Jan. 2017, Invited

  
• On the classification of smooth quandles

  Ishikawa Katsumi

  Friday Seminar on Knot Theory, 28 Oct. 2016, Invited

  
• Smooth quandle structures on closed surfaces

  Ishikawa Katsumi

  The 8th KOOK-TAPU Joint Seminar on Knots and Related Topics & The 10th Graduate Student Workshop on Mathematics, 28 Jul. 2016

  
• Smooth quandle structures on closed surfaces

  Ishikawa Katsumi

  微分トポロジーセミナー（京都大学数学教室）, 07 Jun. 2016, Invited

  
• Quandle cocycle invariants of cabled surface knots

  Ishikawa Katsumi

  Intelligence of Low-dimensional Topology, 20 May 2016, Invited

  
• Cabling formulae of quandle cocycle invariants for surface knots

  Ishikawa Katsumi

  結び目の数学VIII, 25 Dec. 2015

  

External funds: Kakenhi

• Kontsevich不変量と結び目の可逆性

  Grant-in-Aid for Early-Career Scientists

  Basic Section 11020:Geometry-related

  Kyoto University

  石川 勝巳

  From 01 Apr. 2020, To 31 Mar. 2025, Granted

  結び目;Kontsevich不変量;有限型不変量;可逆性;量子不変量

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20K14309/
• On the vanishing of the twisted Alexander polynomial for knots and 3-manifolds

  Grant-in-Aid for Early-Career Scientists

  Basic Section 11020:Geometry-related

  Kyoto University

  石川 勝巳

  From 01 Apr. 2025, To 31 Mar. 2030, Granted

  結び目;3次元多様体;捩れAlexander多項式;ファイバー性;被覆空間

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-25K17252/

Education

Teaching subject(s)

• From 01 Apr. 2024, To 31 Mar. 2025

  Invitation to Modern Mathematics and Mathematical Sciences

  N114, Spring, Institute for Liberal Arts and Sciences, 2
• From 01 Apr. 2023, To 31 Mar. 2024

  Invitation to Modern Mathematics and Mathematical Sciences

  N114, Spring, Institute for Liberal Arts and Sciences, 2
• From 01 Apr. 2022, To 31 Mar. 2023

  Exercises in Geometry I

  3182, Spring, Faculty of Science, 4
• From 01 Apr. 2022, To 31 Mar. 2023

  Invitation to Modern Mathematics and Mathematical Sciences

  N114, Spring, Institute for Liberal Arts and Sciences, 2
• From Apr. 2020, To Mar. 2021

  Invitation to Modern Mathematics and Mathematical Sciences - Basic concepts and their role in various sciences

  Spring, 全学共通科目
• From Apr. 2021, To Mar. 2022

  Invitation to Modern Mathematics and Mathematical Sciences - Basic concepts and their role in various sciences

  Spring, 全学共通科目