Updated on 2025/01/31

写真a

 
HIKAMI KAZUHIRO
 
Organization
Faculty of Mathematics Division of Analysis Associate Professor
School of Sciences Department of Mathematics(Concurrent)
Graduate School of Mathematics Department of Mathematics(Concurrent)
Joint Graduate School of Mathematics for Innovation (Concurrent)
Title
Associate Professor
External link

Degree

  • Doctor of Science

Research Interests・Research Keywords

  • Research theme: conformal algebra

    Keyword: conformal field theory

    Research period: 2008.1 - 2011.12

  • Research theme: quantum topology

    Keyword: quantum invariant, 3-manifold, knots

    Research period: 1999.8 - 2011.6

  • Research theme: quantum integrable system

    Keyword: quantum many-body system, quantum spin chain, quantum group

    Research period: 1992.4 - 2000.6

Papers

  • A note on double affine Hecke algebra for skein algebra on twice-punctured torus

    Hikami K.

    Journal of Geometry and Physics   209   2025.3   ISSN:03930440

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    Publisher:Journal of Geometry and Physics  

    We construct a generalization of the C∨C1-type double affine Hecke algebra for the skein algebra on the twice-punctured torus Σ1,2 using the Heegaard dual of the Iwahori–Hecke operator recently introduced in our previous article. We show that the automorphisms of our algebra correspond to the Dehn twists about the curves on Σ1,2. We also give the cluster algebraic construction of the classical limit of the skein algebra, where the Dehn twists are given in terms of the cluster mutations.

    DOI: 10.1016/j.geomphys.2024.105408

    Scopus

  • Generalized double affine Hecke algebra for double torus Reviewed International journal

    Hikami, K

    LETTERS IN MATHEMATICAL PHYSICS   114 ( 4 )   2024.8   ISSN:0377-9017 eISSN:1573-0530

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Letters in Mathematical Physics  

    We propose a generalization of the double affine Hecke algebra of type-C∨C1 at specific parameters by introducing a “Heegaard dual” of the Hecke operators. Shown is a relationship with the skein algebra on double torus. We give automorphisms of the algebra associated with the Dehn twists on the double torus.

    DOI: 10.1007/s11005-024-01848-2

    Web of Science

    Scopus

  • Torus link T(2s,2t) and (s,t)-log VOA International journal

    Kazuhiro Hikami, Shoma Sugimoto

    arXiv   2023.6

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    Language:English  

    DOI: 10.48550/arXiv.2306.03338

    Repository Public URL: https://hdl.handle.net/2324/7332358

  • Non-semisimple invariants and Habiro's series Invited Reviewed International journal

    @Anna Beliakova, Kazuhiro Hikami

    Topology and Geometry: A Collection of Essays Dedicated to Vladimir G. Turaev   161 - 174   2021.6

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.4171/IRMA/33-1/10

  • DAHA and skein algebra on surface: double-torus knots Reviewed International journal

    Kazuhiro Hikami

    Letters in Mathematical Physics   2019.6

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1007/s11005-019-01189-5

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Presentations

  • 二重アフィンHecke代数とスケイン代数 Invited

    樋上和弘

    スケイン代数とその周辺  2024.10 

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    Event date: 2024.10

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

    Venue:大阪公立大学 I-site なんば   Country:Japan  

  • Skein algebra, cluster algebra, DAHA Invited

    樋上和弘

    東北クラスターセミナー  2023.6 

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    Event date: 2023.6

    Language:Japanese   Presentation type:Public lecture, seminar, tutorial, course, or other speech  

    Venue:東北大学   Country:Japan  

  • 入門:モックテータ関数とムーンシャイン Invited

    樋上和弘

    早稲田整数論セミナー  2022.12 

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    Event date: 2022.12

    Language:Japanese   Presentation type:Public lecture, seminar, tutorial, course, or other speech  

    Venue:Zoom   Country:Japan  

  • 3-manifodls and quantum modular forms Invited International conference

    Kazuhiro Hikami

    AMS spring western virtual sectional meeting: special session "q-series, number theory, and quantum topology"  2022.5 

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    Event date: 2022.5

    Language:English   Presentation type:Oral presentation (general)  

    Venue:Zoom (hosted by American Mathematical Society)   Country:Japan  

  • モックモジュラー形式と量子モジュラー形式 Invited

    樋上和弘

    東北大学理学部数学科 談話会  2021.6 

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    Event date: 2021.6

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:Zoom   Country:Japan  

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MISC

  • モックテータ関数

    樋上 和弘

    数理科学(サイエンス社)   2020.8

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    Language:Japanese   Publishing type:Article, review, commentary, editorial, etc. (scientific journal)  

Professional Memberships

  • 日本物理学会

  • American Mathematical Society

Academic Activities

  • Organizer

    q級数とその周辺  ( Japan ) 2024.3

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    Type:Competition, symposium, etc. 

    Number of participants:31

  • Organizer International contribution

    q-series, quantum modular forms and representation theory  ( Online (http://www.kurims.kyoto-u.ac.jp/~tshun/q2020/) Japan ) 2020.10

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    Type:Competition, symposium, etc. 

    Number of participants:126

  • Organizer International contribution

    Modular Forms and Quantum Knot Invariants  ( Banff International Research Station Canada ) 2018.3

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    Type:Competition, symposium, etc. 

  • Organizer International contribution

    School on Mock Modular Forms and Related Topics  ( Momochi Office Japan ) 2016.11

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    Type:Competition, symposium, etc. 

    Number of participants:48

  • Organizer International contribution

    String, Lattice, and Moonshine  ( Japan ) 2014.12

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    Type:Competition, symposium, etc. 

    Number of participants:40

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Research Projects

  • 量子モジュラー形式の深化と展開

    Grant number:22K01117  2024 - 2026

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)

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    Authorship:Principal investigator  Grant type:Scientific research funding

  • Quantum Modular Forms and their Applications

    Grant number:23K22388  2022.4 - 2027.3

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)

    樋上 和弘, 村上 斉, 藤 博之, 寺嶋 郁二

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    Authorship:Principal investigator  Grant type:Scientific research funding

    結び目や3次元多様体の量子不変量の背景にある幾何学的性質を明らかにしようとする過程において生まれたものが量子モジュラー形式である。2010年頃に提唱された新しい研究対象であり、数学だけでなく超弦理論など物理においてもその重要性が増している。数学・物理のさまざまな手法を取り入れて量子モジュラー形式の数理・幾何構造を確立しその応用研究を目指す。

    CiNii Research

  • 量子モジュラー形式の深化と展開

    Grant number:22H01117  2022 - 2023

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)

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    Authorship:Principal investigator  Grant type:Scientific research funding

  • 幾何的漸化式に基づく量子トポロジーと弦の場の量子構造の数理の究明

    Grant number:20K03931  2020 - 2024

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    藤 博之, 樋上 和弘, 村上 斉, 真鍋 征秀

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    Authorship:Coinvestigator(s)  Grant type:Scientific research funding

    本研究課題では,幾何的漸化式が記述する理論を,行列模型や位相的漸化式,さらに非臨界弦の場の理論の立場から理解を深め,量子トポロジーや結び目の量子不変量などへの新たな応用を探る予定である.
    位相的漸化式は行列模型の解析を超えて,ミラー対称性や超対称ゲージ理論,Kontsevich-Witten理論,体積予想など様々な幾何学や物理学の量子的側面を浮き彫りにし,新たな発展をもたらしてきた.
    この位相的漸化式の発展形として導入された幾何的漸化式もまた新たな幾何学や物理学の背後に潜む量子的側面を明らかにできることが期待され,その中でも弦の場の理論は最も興味深い応用例の一つとなるものと考えている.

    CiNii Research

  • Asymptotic behaviors of quantum invariants of knots and three-manifolds

    Grant number:20K03601  2020 - 2023

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    村上 斉, 樋上 和弘, 藤 博之

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    Authorship:Coinvestigator(s)  Grant type:Scientific research funding

    結び目や3次元多様体の量子不変量は,作用素環論や理論物理を契機に導入されたものであり,20世紀末から盛んに研究されている.特に,近年体積予想を初めとして,量子不変量の漸近挙動と,位相的な性質を結びつける試みが注目を集めている.
    本研究では,量子不変量の典型的な例である,結び目の色付きJones多項式や,3次元多様体のWitten-Reshetikhin-Turaev不変量の漸近挙動を考察し,それを位相的な観点から調べる.

    CiNii Research

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Class subject

  • 微分積分学 II

    2024.10 - 2025.2   Second semester

  • 微分積分学II

    2024.10 - 2025.2   Second semester

  • 数学特論B3

    2024.10 - 2024.11   Fall quarter

  • 微分積分学I

    2024.4 - 2024.9   First semester

  • 微分積分学I (工学)

    2024.4 - 2024.9   First semester

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FD Participation

  • 2011.4   Role:Participation   Title:平成23年度第1回全学FD(新任教員研修)

    Organizer:University-wide

Visiting, concurrent, or part-time lecturers at other universities, institutions, etc.

  • 2021  東北大学 理学研究科  Classification:Intensive course 

    Semester, Day Time or Duration:6月28日〜7月2日

  • 2014  東北大学 情報科学研究科  Classification:Intensive course  Domestic/International Classification:Japan 

    Semester, Day Time or Duration:2015年1月13日~16日

Social Activities

  • モックテータ関数

    2021年新春特別講義「ラマヌジャンと宇宙」 数学協会、東京大学素粒子物理国際研究センター、四日市大学関孝和数学研究所  オンライン(Zoom)  2021.1

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    Audience:General, Scientific, Company, Civic organization, Governmental agency

    Type:Lecture

  • ラマヌジャン:母関数とタクシー数

    九州大学オープンキャンパス  2018.8

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    Audience:Infants, Schoolchildren, Junior students, High school students

    Type:Seminar, workshop

  • ラマヌジャンの最後の手紙

    九州大学「現代数学入門」  西新プラザ  2015.7

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    Audience:General, Scientific, Company, Civic organization, Governmental agency

    Type:Lecture

  • 量子計算のはなし

    九州大学オープンキャンパス  2014.8

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    Audience:Infants, Schoolchildren, Junior students, High school students

    Type:Seminar, workshop

  • 出張講義

    北筑高等学校  2012.8

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    Audience:Infants, Schoolchildren, Junior students, High school students

    Type:Seminar, workshop

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Acceptance of Foreign Researchers, etc.

  • University College Dublin

    Acceptance period: 2022.7   (Period):Less than 2 weeks

    Nationality:United States

    Business entity:Japan Society for the Promotion of Science

  • Emory University

    Acceptance period: 2019.11   (Period):Less than 2 weeks

    Nationality:New Zealand

    Business entity:Japan Society for the Promotion of Science

  • University of Hawaii

    Acceptance period: 2016.11  

    Nationality:Canada

    Business entity:Japan Society for the Promotion of Science

  • Trinity College Dublin

    Acceptance period: 2016.11   (Period):Less than 2 weeks

    Nationality:United States

    Business entity:Japan Society for the Promotion of Science

  • University of Hong Kong

    Acceptance period: 2016.11   (Period):Less than 2 weeks

    Nationality:United States

    Business entity:Japan Society for the Promotion of Science

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Travel Abroad

  • 2019.11

    Staying countory name 1:Germany   Staying institution name 1:DESY

  • 2019.3

    Staying countory name 1:United States   Staying institution name 1:ICERM, Brown University

  • 2019.1

    Staying countory name 1:Austria   Staying institution name 1:Erwin Schrödinger Institute

  • 2018.3

    Staying countory name 1:Canada   Staying institution name 1:Banff International Research Station

  • 2017.12

    Staying countory name 1:Korea, Republic of   Staying institution name 1:National Institute for Mathematical Sciences, Daejeon

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