Koda, Yuya

写真a

Affiliation

Faculty of Economics ( Hiyoshi )

Position

Professor

Related Websites

Contact Address

4-1-1, Hiyoshi, Kohoku, Yokohama, 223-8521, Japan

Career 【 Display / hide 】

  • 2005.04
    -
    2007.09

    JSPS Reasearch Fellow, DC1

  • 2007.10
    -
    2008.03

    JSPS Reasearch Fellow, PD

  • 2008.04
    -
    2008.05

    Keio University, Department of Mathematics, Visiting Scholar

  • 2008.06
    -
    2008.09

    Kogakuin University, Academic Support Center, Lecturer

  • 2008.10
    -
    2009.08

    Tokyo Institute of Technology, Department of Mathematics, Assistant Professor

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Academic Background 【 Display / hide 】

  • 2000.04
    -
    2003.03

    Keio University, 理工学部, 数理科学科

    University, Graduated

  • 2003.04
    -
    2005.03

    Keio University, 大学院理工学研究科, 基礎理工学専攻

    Graduate School, Completed, Master's course

  • 2005.04
    -
    2007.09

    Keio University, 大学院理工学研究科, 基礎理工学専攻

    Graduate School, Completed, Doctoral course

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Academic Degrees 【 Display / hide 】

  • Ph.D. (Science), Keio University, Coursework, 2007.09

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Books 【 Display / hide 】

  • 手を動かしてまなぶ トポロジー《基本群》

    古宇田 悠哉, 裳華房, 2025.12,  Page： 422

    　View Summary

    代数的トポロジーの主要な手法のひとつ──基本群と被覆空間を、じっくり丁寧に解き明かす。基本群の定義やその計算方法を、豊富なオリジナルの図とともに解説し、その威力を十分に体感できるようにした。本書の“華”は、被覆空間のガロア理論を通じて、基本群の理論と被覆空間の理論が表裏一体であることに到達し、大団円を迎えることである。
    　幾何学　（位相空間）と代数学（群）という一見異なる分野が結びつき、美しく調和する基本群と被覆空間の世界。本書で、単なる計算や公式を超えた深い洞察を見出し、数学の奥深さを味わってみませんか。

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Papers 【 Display / hide 】

  • Homotopy classification of knotted defects in bounded domains

    Nozaki Y., Palmer D., Koda Y.

    Letters in Mathematical Physics 115 ( 6 )  2025.12

    ISSN  03779017

    　View Summary

    Nozaki et al. gave a homotopy classification of the knotted defects of ordered media in three-dimensional space by considering continuous maps from complements of spatial graphs to the order parameter space modulo a certain equivalence relation. We extend their result by giving a classification scheme for ordered media in handlebodies, where defects are allowed to reach the boundary. Through monodromies around meridional loops, global defects are described in terms of planar diagrams whose edges are colored by elements of the fundamental group of the order parameter space. We exhibit examples of this classification in octahedral frame fields and biaxial nematic liquid crystals.

  • Quantum enhancement polynomials associated with the canonical two-element tribracket

    Koda Y., Nishimura Y., Sakamoto Y.

    Journal of Knot Theory and Its Ramifications  2025

    ISSN  02182165

    　View Summary

    Quantum enhancement polynomials are invariants for oriented links, defined in association with an algebraic structure called a tribracket. In this paper, we focus on the particular case of the canonical two-element tribracket. We prove that, in that case, the quantum enhancement polynomials can be recovered by five specific polynomials, which we refer to as the universal quantum enhancement polynomials. After presenting several notable properties of these polynomials, we show that they are strictly stronger than the Jones polynomial. Furthermore, we provide computational results for links with up to 10 crossings.

  • The Goeritz groups of (1,1)-decompositions

    Koda Y., Tanaka Y.

    Journal of Topology and Analysis  2025

    ISSN  17935253

    　View Summary

    A (g,n)-decomposition of a link L in a closed orientable 3-manifold M is a decomposition of M by a closed orientable surface of genus g into two handebodies each intersecting the link L in n trivial arcs. The Goeritz group of that decomposition is then defined to be the group of isotopy classes of orientation-preserving homeomorphisms of the pair (M,L) that preserve the decomposition. We compute the Goeritz groups of all (1, 1)-decompositions.

  • Homotopy classification of knotted defects in ordered media

    Nozaki Y., Kálmán T., Teragaito M., Koda Y.

    Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences 480 ( 2300 )  2024.10

    ISSN  13645021

    　View Summary

    We give a homotopy classification of the global defects in ordered media and explain it via the example of biaxial nematic liquid crystals, that is, systems where the order parameter space is the quotient of the three-sphere S 3 by the quaternion group Q. As our mathematical model, we consider continuous maps from complements of spatial graphs to the space S 3 / Q modulo a certain equivalence relation and find that the equivalence classes are enumerated by the six subgroups of Q. Through monodromy around meridional loops, the edges of our spatial graphs are marked by conjugacy classes of Q; once we pass to planar diagrams, these labels can be refined to elements of Q associated with each arc. The same classification scheme applies not only in the case of Q but also to arbitrary groups.

  • Positive flow-spines and contact 3-manifolds

    Ishii I., Ishikawa M., Koda Y., Naoe H.

    Annali di Matematica Pura ed Applicata (Annali di Matematica Pura ed Applicata)  202 ( 5 ) 2091 - 2126 2023.10

    ISSN  03733114

    　View Summary

    A flow-spine of a 3-manifold is a spine admitting a flow that is transverse to the spine, where the flow in the complement of the spine is diffeomorphic to a constant flow in an open ball. We say that a contact structure on a closed, connected, oriented 3-manifold is supported by a flow-spine if it has a contact form whose Reeb flow is a flow of the flow-spine. It is known by Thurston and Winkelnkemper that any open book decomposition of a closed oriented 3-manifold supports a contact structure. In this paper, we introduce a notion of positivity for flow-spines and prove that any positive flow-spine of a closed, connected, oriented 3-manifold supports a contact structure uniquely up to isotopy. The positivity condition is critical to the existence of the unique, supported contact structure, which is also proved in the paper.

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Papers, etc., Registered in KOARA 【 Display / hide 】

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Research Projects of Competitive Funds, etc. 【 Display / hide 】

  • 3次元トポロジーに由来する写像類群の部分群の構造解明

    2024.04
    -
    2028.03

    基盤研究(C), Principal investigator

  • 多面体を用いた３・４次元多様体の微分構造と幾何構造の研究

    2021.04
    -
    Present

    文部科学省・日本学術振興会, 科学研究費補助金 基盤研究（C）, Principal investigator

  • 多面体を用いた３・４次元多様体の微分構造と幾何構造の研究

    2020.04
    -
    2024.03

    基盤研究(C), Principal investigator

  • ３次元多様体のシャドウ複雑度と幾何構造に関する研究

    2017.04
    -
    2021.03

    文部科学省・日本学術振興会, 科学研究費補助金 基盤研究（C）, Principal investigator

  • ヒーガード分解の写像類群の研究

    2014.04
    -
    2017.03

    文部科学省・日本学術振興会, 科学研究費補助金 若手研究（B）, Principal investigator

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Courses Taught 【 Display / hide 】

  • ADVANCED LINEAR ALGEBRA

    2025

  • MATHEMATICS FOR ECONOMICS 2

    2025

  • MATHEMATICS FOR ECONOMICS 1

    2025

  • LINEAR ALGEBRA

    2025

  • CALCULUS

    2025

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Memberships in Academic Societies 【 Display / hide 】

  • The Mathematical Society of Japan, 

    2006
    -
    Present
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Committee Experiences 【 Display / hide 】

  • 2025.07
    -
    Present

    雑誌 `数学' 編集委員長, 日本数学会

  • 2025.04
    -
    2025.06

    雑誌 `数学' 編集委員（常任）, 日本数学会

  • 2024.03
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    Present

    Scientific Editor, Journal of Knot Theory and Its Ramifications

  • 2022.04
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    2023.03

    理学部数学科長, 広島大学

  • 2022.03
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    2023.02

    中国・四国支部 評議員, 日本数学会

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