Updated on 2022/09/29

写真a

 
TAKATA Doman
 
Organization
Academic Assembly Institute of Humanities and Social Sciences KYOIKUGAKU KEIRETU Lecturer
Faculty of Education Mathematical and Natural Sciences Lecturer
Title
Lecturer
External link

Degree

  • 博士(理学) ( 2018.3 )

  • 修士(理学) ( 2015.3 )

Research Interests

  • noncommutative geometry

  • KK-theory

  • C^*-algebra of a Hilbert manifold

  • global analysis

  • infinite-dimensional manifold

  • index theorem

  • loop group

  • topological K-theory

Research Areas

  • Natural Science / Geometry

Research History (researchmap)

  • Niigata University   Lecturer

    2021.4

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  • The University of Tokyo

    2018.4 - 2021.3

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Research History

  • Niigata University   Institute of Humanities and Social Sciences, Academic Assembly   Lecturer

    2021.4

  • Niigata University   Mathematical and Natural Sciences, Faculty of Education   Lecturer

    2021.4

Education

  • Kyoto University   Graduate School of Science   Division of Mathematics

    2015.4 - 2018.3

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  • Kyoto University   Graduate School of Science   Division of Mathematics

    2013.4 - 2015.3

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Professional Memberships

 

Papers

  • An infinite-dimensional index theorem and theHigson–Kasparov–Trout algebra Reviewed

    Doman Takata

    Annals of K-Theory   7 ( 1 )   1 - 76   2022.6

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Mathematical Sciences Publishers  

    DOI: 10.2140/akt.2022.7.1

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  • LT-equivariant index from the viewpoint of KK-theory; Global analysis of Infinite-dimensional Heisenberg Group Reviewed

    Doman Takata

    Journal of Geometry and Physics   150   2020.1

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    Language:English  

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  • An analytic LT-equivariant index and noncommutative geometry Reviewed

    Doman Takata

    Journal of noncommutative geometry   13 ( 2 )   553 - 586   2019.7

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

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  • Noncommutative geometry and an index theory of infinite-dimensional manifolds Reviewed

    Doman Takata

    `Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 1'   1   377 - 381   2018.3

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

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  • A Loop Group Equivariant Analytic Index Theory for Infinite-dimensional Manifolds

    Doman Takata

    2018.3

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    Authorship:Lead author   Language:English   Publishing type:Doctoral thesis  

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  • Naturality of FHT isomorphism Reviewed

    Doman Takata

    Journal of GGT   10   1 - 41   2015.12

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    Language:English  

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MISC

  • FHT 同型とその自然性

    高田土満

    第12回城崎新人セミナー報告集   2015.4

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    Authorship:Lead author  

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Presentations

  • 同変指数の局所化と形式的べき級数環 ~Witten種数の非可換幾何的定式化に向かって~

    高田土満

    東京都立大学・ハイブリッド幾何学セミナー  2022.6 

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    Event date: 2022.6

    Language:Japanese   Presentation type:Oral presentation (general)  

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  • Localized S1-equivariant index of non-compact manifolds and an analytic counterpart of Witten’s equivariant index of loop spaces Invited

    2022.5 

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    Event date: 2022.5

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

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  • An infinite-dimensional index theory and the Higson-Kasparov-Trout algebra

    Doman Takata

    Operator Algebra Seminar  2020.8 

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    Event date: 2020.8

    Language:English   Presentation type:Oral presentation (general)  

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  • Atiyah-Singerの指数定理の無限次元化に向けて(新型コロナウイルス感染症流行のため中止)

    高田土満

    日本数学会2020年度会幾何学分科会一般講演  2020.3 

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    Event date: 2020.3

    Language:Japanese   Presentation type:Oral presentation (general)  

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  • 無限次元多様体のK理論的Poincaré双対

    高田土満

    関西ゲージ理論セミナー  2020.1 

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    Event date: 2020.1

    Language:Japanese   Presentation type:Oral presentation (general)  

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  • An infinite-dimensional index theory and the Higson-Kasparov-Trout algebra

    Doman Takata

    Operator algebra seminar  2019.12 

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    Event date: 2019.12

    Language:English   Presentation type:Oral presentation (general)  

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  • Loop group and an index theory for infinite-dimensional manifolds

    Doman Takata

    Geometry and Topology seminar  2019.4 

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    Event date: 2019.4

    Language:English   Presentation type:Oral presentation (general)  

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  • Towards the infinite-dimensional-version index theorem: the latter half of the assembly map

    Doman Takata

    Noncommutative geometry seminar  2019.3 

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    Event date: 2019.3

    Language:English   Presentation type:Oral presentation (general)  

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  • Towards the infinite-dimensional-version index theorem: Poincaré duality

    Doman Takata

    Noncommutative geometry seminar  2019.2 

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    Event date: 2019.2

    Language:English   Presentation type:Oral presentation (general)  

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  • Towards an infinite-dimensional index theorem Invited

    高田土満

    作用素環の最近の進展  2018.9 

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    Event date: 2018.9

    Language:Japanese   Presentation type:Oral presentation (general)  

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  • 指数定理とその展開 Invited

    高田土満

    ミラー対称性の諸相  2018.9 

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    Event date: 2018.9

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

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  • Towards an infinite-dimensional index theorem Invited

    Doman Takata

    K-theory and index theory  2018.8 

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    Event date: 2018.8

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

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  • 無限次元多様体の解析的指数とKK理論

    高田土満

    松山TGSAセミナー  2018.5 

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    Event date: 2018.5

    Language:Japanese   Presentation type:Oral presentation (general)  

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  • 無限次元多様体の解析的指数とKK理論

    高田土満

    火曜トポロジーセミナー  2018.5 

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    Event date: 2018.5

    Language:Japanese   Presentation type:Oral presentation (general)  

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  • An analytic index theory for infinite-dimensional manifolds and KK-theory Invited

    Doman Takata

    Workshop on Noncommutative Geometry and Representation Theory  2018.5 

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    Event date: 2018.5

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

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  • 無限次元空間の同変指数理論と非可換幾何学

    高田土満

    作用素環セミナー  2018.4 

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    Event date: 2018.4

    Language:Japanese   Presentation type:Oral presentation (general)  

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  • Towards an infinite-dimensional version of the Atiyah-Singer index theorem from the viewpoint of noncommutative geometry Invited

    Doman Takata

    Noncommutative geometry and K-theory at Rits --The fourth China-Japan conference--  2018.3 

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    Event date: 2018.3

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

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  • Towards an infinite-dimensional version of the Atiyah-Singer index theorem from the viewpoint of noncommutative geometry Invited

    Doman Takata

    Gauge theory in Fukuoka  2018.2 

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    Event date: 2018.2

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

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  • Towards an infinite-dimensional version of the Atiyah-Singer index theorem from the viewpoint of noncommutative geometry

    Doman Takata

    EACDFM 2018  2018.1 

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    Event date: 2018.1

    Language:English   Presentation type:Oral presentation (general)  

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  • 非可換幾何学と無限次元多様体上の指数理論 Invited

    高田土満

    幾何学シンポジウム  2017.8 

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    Event date: 2017.8

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

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  • K-theory and noncommutative geometry

    Doman Takata

    Applied algebraic topology 2017  2017.8 

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    Event date: 2017.8

    Language:English   Presentation type:Poster presentation  

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  • Noncommutative geometry and an index theory of infinite-dimensional manifolds

    Doman Takata

    QTS12 and LT10  2017.6 

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    Event date: 2017.6

    Language:English   Presentation type:Oral presentation (general)  

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  • Noncommutative geometry and an index theory for some infinite-dimensional manifolds

    Doman Takata

    Differential topology seminar  2017.3 

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    Event date: 2017.3

    Language:English   Presentation type:Oral presentation (general)  

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  • Infinite dimensional manifolds and noncommutative geometry Invited

    Doman Takata

    HeKKSaGOn German-Japanese university network  2017.3 

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    Event date: 2017.3

    Language:English   Presentation type:Oral presentation (general)  

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  • Towards an infinite-dimensional version of Atiyah-Singer index theorem

    Doman Takata

    Noncommutative geometry seminar  2017.1 

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    Event date: 2017.1

    Language:English   Presentation type:Oral presentation (general)  

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  • Loop 群上のDirac 作用素とFreed-Hopkins-Teleman 同型

    高田土満

    微分トポロジーセミナー  2016.10 

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    Event date: 2016.10

    Language:Japanese   Presentation type:Oral presentation (general)  

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  • ``Dirac operators'' on compact Lie groups and Loop groups

    Doman Takata

    EACDFM 2016  2016.1 

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    Event date: 2016.1

    Language:English   Presentation type:Oral presentation (general)  

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  • 代数・幾何・解析の表現論における交錯とその無限次元化

    高田土満

    異分野・異業種研究交流会2015  2015.10 

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    Event date: 2015.10

    Language:Japanese   Presentation type:Poster presentation  

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  • FHT 同型とその自然性

    高田土満

    信州トポロジーセミナー  2015.7 

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    Event date: 2015.7

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

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  • FHT同型とその自然性

    高田土満

    第12回城崎新人セミナー  2015.2 

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    Event date: 2015.2

    Language:Japanese   Presentation type:Poster presentation  

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  • Seiberg-Witten写像の「Pin(2)同変K理論的写像度」と奇素数位数巡回群の表現論

    高田土満

    関西ゲージ理論セミナー  2021.5 

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    Language:Japanese   Presentation type:Oral presentation (general)  

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Research Projects

  • A study on the Witten genus by C*-algebras of Hilbert manifolds

    Grant number:21K20320  2021.8 - 2023.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Research Activity Start-up  Grant-in-Aid for Research Activity Start-up

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    Grant amount:\3120000 ( Direct Cost: \2400000 、 Indirect Cost:\720000 )

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  • Index theorem of infinite-dimensional manifolds and noncommutative geometry

    Grant number:18J00019  2018.4 - 2021.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for JSPS Fellows  Grant-in-Aid for JSPS Fellows

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    Grant amount:\3640000 ( Direct Cost: \2800000 、 Indirect Cost:\840000 )

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  • 表現論を用いた無限次元空間の指数理論

    Grant number:16J02214  2016.4 - 2018.3

    日本学術振興会  科学研究費助成事業 特別研究員奨励費  特別研究員奨励費

    高田 土満

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    Grant amount:\1300000 ( Direct Cost: \1300000 )

    昨年度と同じ問題を,よりKK理論的な観点から研究した.その問題のモデルはKasparovの結果であるが,それは非コンパクト多様体に局所コンパクト群がproperかつcocompactに作用しているとき,Dirac作用素dの解析的同変指数が定義され,それが,dが作るKホモロジー群の元[d]をdescent homomorphismで送ったものと,群作用からきまるある標準的なKK群の元[c]のKasparov積(Assembly mapによる[d]の像と呼ぶ)で書けることを主張する.昨年度の成果は,Dirac作用素が作るLT同変Kホモロジー群の「元」[D]を(Kホモロジー群の元としてではなくHilbert空間と作用素の組として)構成し,それの素朴な意味でLT同変解析的指数を計算したことにあるが,今年度はその結果をよりKasparovの結果に平行するような形で定式化し直し,Assembly mapの構成に必要なもの構成した.より詳しく言うと,「無限次元空間の関数環のLTによるねじれのない接合積」を新たに構成し,それと昨年構成したLTのねじれ群C^*環のKK群の元として,「[D]のdescent homomorphismによる像」と[c]に対応するK群の元を,(仮想的ではなく本当に)KK群の元として構成し,それらのKasparov積(「Assembly mapの像」と呼べるもの)を計算した.また,解析的指数をKasparovの定義に沿うようにKK群の元として定式化しなおし,「[D]のAssembly mapの像」と一致することを示した.この結果は,Kasparovの結果の無限次元版と言え,論文[Doman Takata:LT-equivariant Index from the Viewpoint of KK-theory]としてarXivで発表してある.

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Teaching Experience (researchmap)

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