Updated on 2022/03/29

写真a

 
KAWAMURA, Tomomi
 
Organization
Graduate School of Mathematics Division of Mathematics Social Mathematics Associate professor
Graduate School
Graduate School of Mathematics
Undergraduate School
School of Science
Title
Associate professor
Contact information
メールアドレス
External link

Degree 2

  1. 博士(数理科学) ( 2000.3   東京大学 ) 

  2. 修士(数理科学) ( 1997.3   東京大学 ) 

Research Interests 2

  1. Low dimensional topology

  2. Knot theory

Research Areas 1

  1. Others / Others  / Geometry

Current Research Project and SDGs 2

  1. 結び目と絡み目のコンコルダンス不変量の幾何学

  2. Estimates of invariants of knots and links using their diagrams

Research History 3

  1. Nagoya University   Graduate school of Mathematics   Associate professor

    2007.4

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    Country:Japan

  2. Aoyama Gakuin University   Department of Physics and Mathematics   Assistant

    2004.4 - 2007.3

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    Country:Japan

  3. Aoyama Gakuin University   Department of Mathematics   Assistant

    2002.4 - 2004.3

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    Country:Japan

Education 3

  1. The University of Tokyo   Graduate School, Division of Mathematical Sciences

    1997.4 - 2000.3

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    Country: Japan

    Notes: Doctor course

  2. The University of Tokyo   Graduate School, Division of Mathematical Sciences

    1995.4 - 1997.3

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    Country: Japan

    Notes: Master course

  3. Ochanomizu University   Faculty of Science   Department of Mathematics

    1991.4 - 1995.3

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    Country: Japan

Professional Memberships 3

  1. Mathematical Society of Japan

    2014.3 - 2015.3

  2. Mathematical Society of Japan

    2011.3 - 2012.3

  3. Mathematical Society of Japan

Awards 1

  1. The MSJ Takebe Katahiro Prizes for Encouragement of Young Researchers

    2003.9   Mathematical Society of Japan  

    Tomomi Kawamura

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    Award type:Award from Japanese society, conference, symposium, etc.  Country:Japan

 

Papers 11

  1. An estimate of the Rasmussen invariant for links and the determination for certain links Invited Reviewed

    Tomomi Kawamura

    Topology and its Applications   Vol. 196 ( part B ) page: 558 - 574   2015.12

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    Authorship:Corresponding author   Language:English   Publishing type:Research paper (scientific journal)  

    Improving the slice-Bennequin inequality shown by Rudolph, we estimate some knot or link invariants, especially the knot invariant defined by Ozsváth and Szabó and the Rasmussen invariant for links introduced by Beliakova and Wehrli. Our argument implies a combinatorial proof of the slice-Bennequin inequality for links. Furthermore we determine such invariants for negative links and certain pretzel knots.

    DOI: 10.1016/j.topol.2015.05.034

  2. The Rasmussen invariants and the sharper slice-Bennequin inequality on knots Reviewed

    Tomomi Kawamura

    Topology   Vol. 46 ( 1 ) page: 29 - 38   2007

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    Authorship:Corresponding author   Language:English   Publishing type:Research paper (scientific journal)  

    Rasmussen introduced a knot invariant based on Khovanov homology theory, and showed that this invariant estimates the four-genus. We compare his result with the sharper slice-Bennequin inequality for knots. Then we obtain a similar estimate of the Rasmussen invariant to this inequality.

  3. Essential cycles in graph divides as a link representation Reviewed

    Tomomi Kawamura

    Tokyo Journal of Mathematics   Vol. 29 ( 2 ) page: 515 - 527   2006.2

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    Authorship:Corresponding author   Language:English   Publishing type:Research paper (scientific journal)  

  4. Links and gordian numbers associated with certain generic immersions of ciecles Reviewed

    Tomomoi Kawamura

    Pacific Journal of Mathematics   Vol. 220 ( 2 ) page: 341 - 357   2005

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    Authorship:Corresponding author   Language:English   Publishing type:Research paper (scientific journal)  

    As an extension of the class of algebraic links, A'Campo, Gibson, and Ishikawa constructed links associated to immersed compact one-manifolds in a two-dimensional disk, and particularly determined the gordian numbers for links of immersed arcs. We determine the gordian numbers for links associated with certain immersed circles.

  5. Links associated with generic immersions of graphs Reviewed

    Tomomi Kawamura

    Algebraic and Geometric Topology   Vol. 4   page: 571 - 594   2004

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    Authorship:Corresponding author   Language:English   Publishing type:Research paper (scientific journal)  

    As an extension of the class of algebraic links, A'Campo, Gibson, and Ishikawa constructed links associated to immersed arcs and trees in a two-dimensional disk. By extending their arguments, we construct links associated to
    immersed graphs in a disk, and show that such links are quasipositive.

  6. Quasipositivity of links of divides and free divides Reviewed

    Tomomi Kawamura

    Topology and Its Applications   Vol. 125 ( 1 ) page: 111 - 123   2002.10

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    Authorship:Corresponding author   Language:English   Publishing type:Research paper (scientific journal)  

  7. On unknotting numbers and four-dimensional clasp numbers of links Reviewed

    Tomomi Kawamura

    Proceedings of the American Mathematical Society   Vol. 130 ( 1 ) page: 243 - 252   2002.1

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    Authorship:Corresponding author   Language:English   Publishing type:Research paper (scientific journal)  

  8. Four-dimensional invariants of links and the adjunction formula Reviewed

    Tomomi Kawamura

    J. Knot Theory Ramifications   Vol. 11 ( 3 ) page: 323 - 340   2002

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    Authorship:Corresponding author   Language:English   Publishing type:Research paper (scientific journal)  

  9. Relations among the lowest degree of the Jones polynomial and geometric invariants for a closed positive braid Reviewed

    Tomomi Kawamura

    Commentarii Mathematici Helvetici   Vol. 77 ( 1 ) page: 125 - 132   2002

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    Authorship:Corresponding author   Language:English   Publishing type:Research paper (scientific journal)  

  10. Lower bounds for the unknotting numbers of the knots obtained from certain links Reviewed

    Tomomi Kawamura

    Proceeding of the Conference Knots in Hellas 1998   Vol. 24   page: 203 - 207   2000

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    Authorship:Corresponding author   Language:English   Publishing type:Research paper (international conference proceedings)  

  11. The unknotting numbers of 10_{139} and 10_{152} are 4 Reviewed

    Tomomi Kawamura

    Osaka Journal of Mathematics   Vol. 35 ( 3 ) page: 539 - 546   1998.9

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    Authorship:Corresponding author   Language:English   Publishing type:Research paper (scientific journal)  

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Books 1

  1. 日本の現代数学 新しい展開を目指して

    小川卓克,斎藤毅,中島啓(編者),著者多数( Role: Joint author ,  結び目理論外見重視派)

    数学書房  2010.6  ( ISBN:978-4-903342-17-7

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    Total pages:241   Responsible for pages:66--80   Language:Japanese

MISC 1

  1. Integral region choice problems on link diagrams

    Tomomi Kawamura

    arXiv     2021.3

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    Authorship:Corresponding author   Language:English   Publishing type:Internal/External technical report, pre-print, etc.  

Presentations 13

  1. Integral region choice problems on link diagrams

    Tomomi Kawamura

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    Event date: 2019.3

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

    Shimizu introduced a region crossing change unknotting operation for knot diagrams. As extensions, two integral region choice problems are proposed and the existences of solutions of the problems are shown for all non-trivial knot diagrams by Ahara and Suzuki, and Harada. We relate both integral region choice problems with an Alexander index for regions of a link diagram, and discuss the problems on link diagrams.

  2. Integral region choice problems on link diagrams

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    Event date: 2018.12

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

    Shimizu introduced a region crossing change unknotting operation for knot diagrams. As extensions, two integral region choice problems are proposed and the existences of solutions of the problems are shown for all non-trivial knot diagrams by Ahara and Suzuki, and Harada.
    We relate both integral region choice problems with an Alexander index for regions of a link diagram, and discuss the problems on link diagrams.

  3. An estimate of the Rasmussen invariant for links and the determination for certain links International conference

    Tomomi Kawamura

    International Conference on Topology and Geometry 2013 Joint with the 6th Japan-Mexico Topology Symposium 

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    Event date: 2013.9

    Language:English   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

    We estimate the knot invariant defined by Ozsv\'{a}th and Szab\'{o} and the Rasmussen invariant for links introduced by Beliakova and Wehrli. We determinate such invariants for negative links and certain Pretzel knots.

  4. 絡み目の整数値不変量のベネカン不等式の精密化

    川村友美

    研究集会「接触構造・特異点・微分方程式およびその周辺」 

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    Event date: 2012.1

    Language:Japanese   Presentation type:Oral presentation (invited, special)  

    Venue:鹿児島大学理学部   Country:Japan  

    接触構造の研究成果として有名なベネカン不等式と類似した評価式が多くの絡み目不変量に対して成立し精密化もなされている.本講演ではとくにスライスオイラー数、ラスムッセン不変量、オズバスとザボーの結び目不変量についての講演者の結果を紹介し、例として負の絡み目について不変量を決定する.

  5. An estimate of the Rasmussen invariant for links

    Tomomi Kawamura

    Knots, Contact Geometry and Floer Homology, Tambara workshop 

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    Event date: 2010.5

    Language:English   Presentation type:Oral presentation (general)  

    Country:Japan  

  6. 絡み目のラスムッセン不変量のベネカン不等式に類似した評価式

    川村 友美

    2009 日本数学会 秋季総合分科会 トポロジー分科会 

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    Event date: 2009.9

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

    Beliakova と Wehrli によって絡み目不変量に拡張された Rasmussen 不変量について,絡み目射影図から得られるデータによる評価式を与えた.これは,結び目の Rasmussen 不変量についてのベネカン不等式より強い下からの評価を与え,さらに(スライス)ベネカン不等式も同じ議論によって改良することに成功した.

  7. An estimate of the Rasmussen invariant for links

    The third East Asian School of Knots and Related Topics 

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    Event date: 2007.2

    Language:English   Presentation type:Oral presentation (general)  

    Country:Japan  

    Improving the slice-Bennequin inequality shown by Rudolph,
    we estimate some knot or link invariants, especially
    the knot invariant defined by Ozsvath and Szabo and the Rasmussen invariant for links introduced by Beliakova and Wehrli.

  8. Various Bennequin inequalities on link invariants

    Intelligence of Low Dimensional Topology 

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    Event date: 2006.7

    Language:English   Presentation type:Oral presentation (general)  

    Country:Japan  

    Improving the slice-Bennequin inequality shown by Rudolph, we estimate some knot or link invariants, especially the knot invariant defined by Ozsvath and Szabo and the Rasmussen invariant for links introduced by Beliakova and Wehrli.

  9. Various Bennequin inequalities on knot concordance invariants

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    Event date: 2006.2

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

    We estimate certain integer-valued knot concordance invariants using diagram invariants. The obtained result is stronger than the Bennequin type inequalities shown by Livingston, Plamenevskaya, and Shumakovitch. Furthermore,
    we improve the slice-Bennequin inequality and the Bennequin unknotting inequality.

  10. Various Bennequin inequalities on knot concordance invariants International conference

    NZ-Japan Knot Theory Conference 

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    Event date: 2006.1

    Language:English   Presentation type:Oral presentation (general)  

    We estimate the Rasmussen invariant, the Ozsvath-Szabo's knot invariant, and other knot concordance invariants.

  11. The Rasmussen invariants and the sharper slice-Bennequin inequality on knots

     More details

    Event date: 2005.8

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

    Rasmussen introduced a knot invariant based on Khovanov homology theory, and showed that this invariant estimates the four-genus. We compare his result with the sharper slice-Bennequin inequality for knots. Then we obtain a similar estimate of the Rasmussen invariant to this inequality.

  12. 絡み目表記としてのグラフディバイドにおけるサイクルの必要性

    川村友美

    日本数学会2005年度年会トポロジー分科会 

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    Event date: 2005.3

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

  13. 絡み目表記としてのグラフディバイドにおけるサイクルの必要性

    川村友美

    研究集会「結び目のトポロジーVII」 

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    Event date: 2004.12

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

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KAKENHI (Grants-in-Aid for Scientific Research) 3

  1. Geometry on concordance invariants of knots and links

    Grant number:24540074  2012.4 - 2018.3

    Kawamura Tomomi

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    Authorship:Principal investigator  Grant type:Competitive

    Grant amount:\5200000 ( Direct Cost: \4000000 、 Indirect Cost:\1200000 )

    A knot or link is a closed curve or its copies in the 3-dimensional space. An invariant of a knot or link is the number or something representing how complex it is. Many invariants have been constructed.
    In this research, we determine the Rasmussen invariant and the Ozsvath-Szabo invariant for certain pretzel knots. Furthermore we show a bridge-replacing move induced on knot diagrams is as useful in computing the Euler characteristic of a link, a kind of link invariants, as the genus of a knot, a kind of knot invariants.

  2. 結び目不変量の射影図による評価とその幾何学的意味

    Grant number:20740035  2008.4 - 2012.3

    科学研究費補助金  若手研究(B)

    川村 友美

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    Authorship:Principal investigator  Grant type:Competitive

  3. ディバイド絡み目の拡張と準正絡み目および代数曲線の関係について

    Grant number:15740044  2003.4 - 2006.3

    科学研究費補助金  若手研究B

    川村 友美

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    Authorship:Principal investigator  Grant type:Competitive

 

Teaching Experience (On-campus) 30

  1. Calculus I

    2021

  2. Complex Analysis

    2021

  3. Calculus II

    2021

  4. Calculus II

    2020

  5. 微分積分学Ⅰ

    2020

  6. 幾何学概論I

    2019

  7. 幾何学続論

    2019

  8. 数学通論II

    2019

  9. 幾何学概論I

    2018

  10. 幾何学続論

    2018

  11. 幾何学概論I

    2017

  12. 幾何学続論

    2017

  13. 微分積分学II

    2017

  14. 微分積分学I

    2017

  15. 微分積分学II

    2016

  16. Topics in Topology I

    2016

  17. 微分積分学I

    2016

  18. 複素関数論

    2014

  19. 幾何学続論/幾何学概論I

    2014

  20. 数理科学展望I

    2013

  21. 幾何学続論/幾何学概論I

    2013

  22. 微分積分学II

    2012

  23. 微分積分学I

    2012

  24. 数学演習III, IV

    2011

  25. Calculus I

    2011

  26. Calculus II

    2011

  27. 数学研究EII

    2008

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    卒業研究

  28. 幾何学続論/幾何学概論I

    2008

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    多様体のトポロジー

  29. 数学研究EI

    2008

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    卒業研究

  30. 幾何学特論I

    2007

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Teaching Experience (Off-campus) 3

  1. 低次元位相幾何学

    2012.4 - 2013.3 Nara Women's University)

  2. 微分積分学IIおよび数学演習

    2009.4 - 2010.3 Nagoya Institute of Technology)

  3. 幾何学特別講義(結び目理論)

    2008.4 - 2009.3 Hokkaido University)