TAMAKI DAI

Academic Assembly School of Science and Technology Institute of Science

Faculty of Science Department of Mathematics Course of Mathematical Sciences 

Professor 

Degree

  • Ph.D. in Mathematics, University of Rochester (USA)

Research Keyword

    loop space, operad, discrete Morse theory, homotopy group, model category, classifying space, category and functor, homology

Field Of Study

  • Geometry, homotopy theory

Mail Address

    rivulus★shinshu-u.ac.jp

Career

  • 2015 - 2015
    Tokyo Metropolitan University, lecturer
  • 2010 - 2010
    京都大学大学院理学研究科 非常勤講師
  • 2009 - 2009
    琉球大学理学部 非常勤講師
  • 2004 - 2004
    東京大学大学院数理科学研究科 非常勤講師
  • 2003 - 2003
    京都大学大学院理学研究科 非常勤講師
  • 1997 - 1997
    九州大学大学院数理学研究科 非常勤講師

Educational Background

  • 1989 - 1993, University of Rochester
  • 1989 - 1993, University of Rochester, Graduate School of Mathematics, Mathematics
  • 1989 - 1993, Kyoto University, Graduate School, Division of Natural Science, Mathematics
  • 1987 - 1989, Kyoto University, Graduate School, Division of Natural Science, Mathematics
  • 1983 - 1987, Kyoto University, Faculty of Science, Mathematics

Paper

  • Stellar stratifications on classifying spaces
    Dai Tamaki, Hiro Lee Tanaka
    Trends in Mathematics, 287-313, 2019, Refereedリポジトリ電子ジャーナル
  • Cellular stratified spaces
    Dai Tamaki
    Combinatorial and Toric Homotopy: Introductory Lectures. Lecure Notes Series, Institute for Mathematical Sciences, National University of Singapore., 35, 305-435, 2018, Refereedリポジトリ電子ジャーナル
  • Discrete Morse theory and classifying spaces
    Vidit Nanda, Dai Tamaki, Kohei Tanaka
    Advances in Mathematics, 340, 723-790, 2018, Refereedリポジトリ電子ジャーナル
  • Totally normal cellular stratified spaces and applications to the configuration space of graphs
    Mizuki Furuse, Takashi Mukouyama, Dai Tamaki
    Topological Methods in Nonlinear Analysis, 45, 169-214, Mar. 2015, RefereedWebofScienceリポジトリ電子ジャーナル
  • Higher topological complexity and its symmetrization
    Ibai Basabe, Jesus Gonzalez, Yuli Rudyak, Dai Tamaki
    Algebraic and Geometric Topology, 14, 2103-2124, 2014, RefereedWebofScienceリポジトリ電子ジャーナル
  • Twisting Segal's K-homology theory
    Dai Tamaki
    Noncommutative Geometry and Physics, 3, 177-195, 2013リポジトリ電子ジャーナル
  • Two-sided bar constructions for partial monoids and applications to K-homology
    Dai Tamaki
    Noncommutative Geometry and Physics, 3, 197-235, 2013リポジトリ電子ジャーナル
  • The Salvetti complex and the little cubes
    Dai Tamaki
    Journal of European Mathematical Society, 14, 801-840, 2012, RefereedWebofScienceリポジトリ電子ジャーナル
  • On the homology of configuration spaces associated to centers of mass
    Dai Tamaki
    Arrangements of hyperplanes---{S}apporo 2009, 62, 417-457, 2012, Refereedリポジトリ
  • On the $E^1$-term of the gravity spectral sequence
    Dai Tamaki
    Geometry and Topology Monographs, 10, 341-376, 2006, Refereed
  • Homology operations and v(n)-Bockstein operations
    D. Tamaki
    Topology and its Applications, 128(2-3), 209-229, 2003, RefereedWebofScience
  • Some cohomotopy groups of suspended projective planes
    H. Kachi, J. Mukai, T. Nozaki, Y. Sumida, D. Tamaki
    Mathematical Journal of Okayama University, 43, 105-121, 2002, Refereed
  • The fiber of Freudenthal suspension and Morava K-theory of $\Omega^kS^{2\ell+1}$
    Dai Tamaki
    Contemporary Mathematics, 293, 299-329, 2002, Refereed
  • Little cubes and homotopy theory
    Dai Tamaki
    Morphismos, 5, 33-60, 2000, Refereed
  • A Dual Rothenberg-Steenrod spectral sequence
    Dai Tamaki
    Topology, 33, 631-662, 1994, Refereed
  • Stable retraction of CW-complexes whose cohomologies are small exterior algebras
    Dai Tamaki
    Journal of Mathematics of Kyoto University, 33, 1097-1102, 1993, Refereed

MISC

  • Category theory and topology
    Dai Tamaki
    現代思想, Jul. 2020, Invited
    Lead, Last, Corresponding
  • ホモトピーという考え方の拡がり
    玉木 大
    数理科学, (5月号), May 2019
  • 代数的トポロジー (特集 目に見えない図形を扱うには) -- (代数のことばで幾何を扱う)
    玉木 大;
    数学セミナー, 56(1), 32-35, Jan. 2017
  • 位相 (特集 現代数学の発想)
    玉木 大;
    数学セミナー, 53(4), 28-33, Apr. 2014
  • 被覆という考え方 (特集 被覆のはなし)
    玉木 大;
    数学セミナー, 52(1), 13-17, Jan. 2013
  • トポロジーは応用できるか?
    玉木 大;
    数学通信, 16(4), 16-27, Feb. 2012
  • Combinatorial Configuration Spaces
    Dai Tamaki
    Proceedings of 2011 International Symposium on Nonlinear Theory and its Applications, 2000--2003, 2011, Refereed
  • エレガントな解答をもとむ 解答--出題 2008年1月号
    西山 豊; 玉木 大;
    数学セミナー, 47(4), 94-100, Apr. 2008
  • エレガントな解答をもとむ 解答 出題2006年7月号
    矢ヶ部 巖; 玉木 大;
    数学セミナー, 45(10), 88-92, Oct. 2006
  • エレガントな解答をもとむ 解答 出題 2005年9月号
    渡辺 守; 玉木 大;
    数学セミナー, 44(12), 92-97, Dec. 2005
  • エレガントな解答をもとむ
    清宮 俊雄; 大島 邦夫; 玉木 大;
    数学セミナ-, 40(4), 86-91, Apr. 2001
  • エレガントな解答をもとむ
    玉木 大; 山田 裕史; 今井 貞三;
    数学セミナ-, 40(1), 100-108, Jan. 2001

Books and other publications

  • Fiber bundles and homotopy
    Dai Tamaki
    World Scientific., - 2021
    ISBN:9789811237997
  • ファイバー束とホモトピー
    玉木大著
    森北出版, - 2020
    ISBN:9784627054615
  • 広がりゆくトポロジーの世界
    玉木 大, Single work
    現代数学社, Nov. 2012
  • Geometry and Topology Monographs 13
    Norio Iwase, Toshitake Kohno, Ran Levi, Dai Tamaki, Jie Wu, Joint work, Groups, homotopy and configuration spaces (Tokyo)
    Mathematical Sciences Publishers, 2008
  • Generalized Cohomology
    Akira Kono, Dai Tamaki, Joint work
    The American Mathematical Society, 2006
  • 岩波講座 現代数学の展開 「一般コホモロジー」
    河野明, 玉木大, Joint work
    岩波書店, 2002

Lectures, oral presentations, etc.

  • Cotorsion pairs in Hopfological algebra
    Dai Tamaki
    Annual conference on homotopy theory, 06 Nov. 2021
  • Applications of functor homology to weighted networks
    Dai Tamaki
    The Week of Applied Mathematical Modelling, 09 Oct. 2019
  • Stratifications on classifying spaces of acyclic categories
    Dai Tamaki
    Mapping Spaces in Algebraic Topology, 30 Aug. 2018, Invited
  • Functorial discrete Morse theory
    Dai Tamaki
    Braid Groups, Configuration Spaces, and Homo- topy Theory, 25 Jul. 2018, Invited
  • Stratifications on classifying spaces of categories
    Dai Tamaki
    7th East Asian Conference on Algebraic Topology, 03 Dec. 2017, Invited
  • Combinatorial gradient flows on cell complexes
    Dai Tamaki
    第12回 鹿児島 代数・解析・幾何学セミナー, 15 Feb. 2017, Invited
  • A combinatorial model for graph braid groups
    Dai Tamaki
    The 2nd mini workshop on knot theory, 16 Dec. 2016, IBS Center for Geometry and Physics, Pohang, Korea, Invited
  • An introduction to directed homotopy theory
    Dai Tamaki
    代数, 論理, 幾何と情報科学研究集会, 28 Aug. 2016, Invited
  • 小圏の分類空間とその応用
    玉木 大
    第16回JMO夏季セミナー, 23 Aug. 2016, 数学オリンピック財団, Invited
  • Configuration spaces and homotopy theory
    Dai Tamaki
    日本数学会年会, 18 Mar. 2016, 日本数学会, Invited
  • Discrete Morse theory and classifying spaces
    Dai Tamaki
    Braids, Configuration Spaces, and Quantum Topology, 10 Sep. 2015, Invited
  • Discrete Morse theory and classifying spaces of 2-categories
    Dai Tamaki
    Workshop on Applied Topology, 21 Aug. 2015, Invited
  • トポロジカル相からK理論へ
    Dai Tamaki
    Summer School 数理物理 2014, 29 Aug. 2014, Invited
  • Discrete Morse theory a la Cohen-Jones-Segal
    Dai Tamaki
    Workshop on Algebraic Topology and its Applications, 08 Aug. 2014, Invited
  • Cellular stratified spaces and their applications II
    Dai Tamaki
    Workshop on Algebraic Topology and its Applications, 07 Aug. 2014, Invited
  • Cellular stratified spaces and their applications I
    Dai Tamaki
    Workshop on Algebraic Topology and its Applications, 06 Aug. 2014, Invited
  • On parametrized functors
    Dai Tamaki
    The Fifth East Asian Conference on Algebraic Topology, 04 Dec. 2013, Invited
  • K-theory and topological phases
    Dai Tamaki
    トポロジカルオーダー勉強会, 25 Nov. 2013, Invited
  • 本当にモデル圏でいいのか?
    Dai Tamaki
    SMART研究会「応用現代幾何学」, 05 Sep. 2013, Invited
  • Applications of cellular stratified spaces
    Dai Tamaki
    International Conference on Topology and Geometry 2013, 02 Sep. 2013, Invited
  • Some applications of cellular stratified spaces
    Dai Tamaki
    Applied Topology, 23 Jul. 2013, Invited
  • An invitation to topology
    Dai Tamaki
    The International Kasetsart Univerisity Science and Technology Annual Research Symposium, 28 Mar. 2013, Invited
  • Cellular stratified spaces III
    Dai Tamaki
    Fukuoka Homotopy Theory Seminar, 13 Jan. 2013, Not invited
  • Bicategories and topological categories in combinatorial algebraic topology
    Dai Tamaki
    Shinshu Applied Topology Seminar, 23 Nov. 2012, Not invited
  • A Salvetti-type model for configuration spaces
    Dai Tamaki
    Applied and computational topology: ATMCS 5, Jul. 2012, Not invited
  • Stellar stratified spaces
    Dai Tamaki
    福岡ホモトピー論セミナー, 06 Jan. 2012, Not invited
  • A user’s guide to cellular stratified spaces
    Dai Tamaki
    Applied Topology, Sep. 2011, Invited
  • Combinatorial configuration spaces
    Dai Tamaki
    2011 International Symposium on Nonlinear Theory and its Applications, Sep. 2011, Invited
  • Combinatorial models for configuration spaces
    Dai Tamaki
    RIMS研究集会変換群の幾何と組合せ論, Jun. 2011, Not invited
  • Constructing bicategories of enriched categories
    Dai Tamaki
    代数幾何とホモトピー論の新展開, Dec. 2010
  • A homotopy colimit spectral sequence for Hochschild and Baues-Wirsching cohomologies
    Dai Tamaki
    International Conference Japan-Mexico on Topology and its Applications, Sep. 2010, Invited
  • Combinatorial configuration spaces
    Dai Tamaki
    第57回 トポロジーシンポジウム, Aug. 2010, Invited
  • Combinatorial configuration spaces
    Dai Tamaki
    京都大学数学教室談話会, Jul. 2010, Invited
  • Constructing bicategories of enriched categories
    Dai Tamaki
    Workshop(s): Lefschetz fibration and category theory, Jun. 2010, Invited
  • もっと数学にWWWを活用するには?
    Dai Tamaki
    Workshop(s): Lefschetz fibration and category theory, Jun. 2010, Invited
  • On Hochschild-Mitchell and Baues-Wirsching cohomologies for diagrams
    Dai Tamaki
    (非)可換代数とトポロジー, Mar. 2010, Invited
  • Enriched stacks and duality
    Dai Tamaki
    第3回東アジア代数的トポロジーシンポジウム, Dec. 2009
  • A homotopy colimit spectral sequence for Hochschild homology
    Dai Tamaki
    ホモトピー論シンポジウム, Nov. 2009, Invited
  • Homotopy colimits for enriched categories
    Dai Tamaki
    第6回静岡代数学セミナー, Nov. 2009, Invited
  • Enriched stacks and duality
    Dai Tamaki
    Category theory, computer science and topology, Oct. 2009, Invited
  • Iterated loop spaces and oriented matroids
    Dai Tamaki
    MSJ-SI conference on arrangements of hyperplanes, Aug. 2009, Invited
  • On classifying spaces of partially defined algebraic structures
    Dai Tamaki
    第4回代数・解析・幾何学セミナー, Feb. 2009, Invited
  • Twisting Segal's K-homology theory
    Dai Tamaki
    Braids and Mapping Class Groups, Dec. 2008, Invited
  • Twisting Segal's K-homology theory
    Dai Tamaki
    ホモトピー論シンポジウム, Dec. 2008
  • A homotopical introduction to twisted K-theory
    Dai Tamaki
    Noncommutative Geometry and Physics 2008, Feb. 2008, Invited
  • Hyperplane arrangements for iterated loop spaces
    Dai Tamaki
    研究集会「超平面配置のさまざまな側面」, Feb. 2008, Invited
  • Iterated loop spaces and oriented matroids
    Dai Tamaki
    International Conference on Topology and its Applications, Dec. 2007, Invited
  • The little cubes and the Salvetti complex
    Dai Tamaki
    第1回東アジア代数的トポロジーシンポジウム, Nov. 2007, Invited
  • 組み合せ論とホモトピー論はより親密になれるか?
    Dai Tamaki
    研究集会「NYメィツの集い」, Mar. 2007
  • Oriented n-matroid and little n-cubes
    Dai Tamaki
    研究集会「空間の代数的・幾何学的モデルの展望」, Sep. 2006, Invited
  • Homology theory and categorification
    Dai Tamaki
    第2回城崎新人セミナー, Feb. 2005, Invited
  • On the E1-term of the gravity spectral sequence
    Dai Tamaki
    第3回日本-メキシコ トポロジーシンポジウム, Dec. 2004, Invited
  • 空間のモデルと準ファイバー空間
    Dai Tamaki
    指数定理とその可能性II, Aug. 2004, Invited
  • On the E1-term of the gravity spectral sequence
    Dai Tamaki
    Workshop on Geometry and Topology of Configuration Spaces, Jul. 2004, Invited
  • Gravity filtration on little cubes revisited
    Dai Tamaki
    研究集会「Lusternik-Schnirelmann categoryとその周辺」, Dec. 2003, Invited
  • Little cubes in homotopy theory
    Dai Tamaki
    京都大学数学教室談話会, Nov. 2003, Invited
  • A configuration space model for the tower of higher order suspensions
    Dai Tamaki
    研究集会「空間の代数的モデルとその応用」, Sep. 2002, Invited
  • On higher order suspensions
    Dai Tamaki
    松江トポロジー国際会議, Jun. 2002
  • 高次懸垂写像について
    Dai Tamaki
    岡山理科大学談話会, Mar. 2002, Invited
  • Higher order Freudenthal suspension and homology of iterated loop spaces
    Dai Tamaki
    ホモトピー論シンポジウム, Nov. 2001
  • Higher order Freudenthal suspension and Morava K-theory of iterated loop spaces
    Dai Tamaki
    Singapore International Symposium on Topology and Geometry, Jul. 2001
  • Constructing cobar spectral sequences for the fiber of iterated Freudenthal suspension
    Dai Tamaki
    ロチェスター大学トポロジーセミナー, Dec. 2000, Invited
  • A cobar spectral sequence for the fiber of the iterated Freudenthal suspension
    Dai Tamaki
    ジョンズ・ホプキンス大学トポロジーセミナー, Dec. 2000, Invited
  • 交差ホモトピー群について
    Dai Tamaki
    京都トポロジーセミナー, Jul. 2000, Invited
  • On vn-Bockstein operations
    Dai Tamaki
    ジョンズ・ホプキンス大学JAMIセミナー, Mar. 2000, Invited
  • Anatomy of Dp(X)
    Dai Tamaki
    研究集会「多様体とホモトピー」, Dec. 1998, Invited
  • Comparing cobar spectral sequences I, II
    Dai Tamaki
    研究集会「モデル理論と有理ホモトピー論」, Dec. 1998, Invited
  • 小立方体のなす空間とその応用
    Dai Tamaki
    東京都立大学数学教室談話会, Nov. 1997, Invited
  • cobar型Eilenberg-Moore spectral sequenceの一意性について
    Dai Tamaki
    岡山理科大学談話会, Nov. 1997, Invited
  • Configuration space of little cubes and its applications
    Dai Tamaki
    九州大学大学院数理学研究科談話会, Oct. 1997, Invited
  • vn-Bocksteins on Dp(X)
    Dai Tamaki
    第1回日本-メキシコ トポロジーシンポジウム, Jul. 1997, Invited
  • Morava K-theory of iterated loop spaces and related topics
    Dai Tamaki
    福岡ホモトピー論セミナー, May 1995, Invited
  • On the convergence problem of cobar-type spectral sequence
    Dai Tamaki
    トポロジーシンポジウム, Jul. 1993, Invited
  • Stable retractions of CW-complexes whose cohomologies are small exterior algebras
    Dai Tamaki
    ホモトピー論研究集会, Dec. 1988, Invited

Courses

  • トポロジー
    Shinshu University
  • 幾何学
    Shinshu University

Affiliated academic society

  • The Mathematical Society of Japan
  • The American Mathematical Society

Research Themes

  • 分野を超えて数学を語るコミュニティを創りたい!
    14 May 2022
  • ホプフォロジカル代数のホモトピー論的研究
    科学研究費補助金, 基盤研究 (C) (一般)
    01 Apr. 2020 - 31 Mar. 2021
  • 結び目と3次元多様体の量子トポロジー
    科学研究費補助金, 基盤研究 (A)
    01 Apr. 2018 - 31 Mar. 2019
  • 離散モース理論の精密化による配置空間のモデルの構築
    科学研究費補助金, 基盤研究 (C)
    01 Apr. 2018 - 31 Mar. 2019
  • 離散モース理論の精密化による配置空間のモデルの構築
    科学研究費補助金, 基盤研究 (C)
    01 Apr. 2015 - 31 Mar. 2019
  • 離散モース理論の精密化による配置空間のモデルの構築
    科学研究費補助金, 基盤研究 (C)
    01 Apr. 2015 - 31 Mar. 2019
  • 離散モース理論の精密化による配置空間のモデルの構築
    科学研究費補助金, 基盤研究 (C)
    01 Apr. 2015 - 31 Mar. 2016
  • Construction of a new model for configuration spaces by means of discrete Morse theory
    Grant-in-Aid for Scientific Research
    2015 - 2019
  • 代数的トポロジー国際セミナー
    29 Jul. 2014 - 12 Aug. 2014
  • 組み合せ論的手法による配置空間のトポロジーの研究
    科学研究費補助金, 基盤研究 (C)
    01 Apr. 2011 - 31 Mar. 2015
  • Combinatorial mathods in the study of topology of configuration spaces and their applications
    Grant-in-Aid for Scientific Research
    2011 - 2014
  • 代数的トポロジー文献案内
    科学研究費補助金, 研究成果公開促進費
    01 Apr. 2010 - 31 Mar. 2011
  • ゲージ理論とホモトピー論
    科学研究費補助金, 基盤研究 B
    01 Apr. 2007 - 31 Mar. 2011
  • モデル圏における非安定高次周期性の研究
    科学研究費補助金, 基盤研究 C
    01 Apr. 2005 - 31 Mar. 2009
  • On unstable higher periodicity phenomena in model categories
    Grant-in-Aid for Scientific Research
    2005 - 2008
  • 高次懸垂写像の組み合わせ論的モデルによるホモトピー群の大域的構造の研究
    科学研究費補助金, 若手研究 B
    01 Apr. 2002 - 31 Mar. 2005
  • The study of global structure of unstable homotopy groups by higher EHP sequence
    Grant-in-Aid for Scientific Research
    2002 - 2004
  • 科学研究費補助金, 奨励研究 A
    01 Apr. 1996 - 31 Mar. 1997
  • 科学研究費補助金, 奨励研究 A
    01 Apr. 1995 - 31 Mar. 1996
  • 科学研究費補助金, 奨励研究 A
    01 Apr. 1994 - 31 Mar. 1995
  • Construction of spectral sequences for loop spaces
  • Homotopy theory of Hopfological algebra
  • The study of the $v_n$-Bockstein operations on the homology of loop spaces

Academic Contribution Activities

  • 現代数学勉強会
    Planning etc
    現代数学勉強会, 上田市中央公民館, 01 Apr. 2016

Acceptance of international students

  • 2009, 1

Acceptance of research students

  • Apr. 2010 - Mar. 2011, 境圭一, 日本, 東京大学大学院数理科学研究科, 結び目のなす空間について
  • 01 Apr. 2017 - 31 Mar. 2018, 小原まり子, 日本, 東北大学大学院理学研究科博士課程, 代数的K理論
  • 01 Apr. 2016 - 31 Mar. 2017, 小原まり子, 日本, 東北大学大学院理学研究科博士課程, 代数的K理論
  • 01 Apr. 2020 - 31 Mar. 2021, 阿部翠空星, 日本, 埼玉大学大学院理工学研究科博士課程, 結び目理論
  • 01 Apr. 2020 - 31 Mar. 2021, 小原まり子, 日本, 東北大学大学院理学研究科博士課程, 代数的K理論
  • 01 Apr. 2019 - 31 Mar. 2020, 小原まり子, 日本, 東北大学大学院理学研究科博士課程, 代数的K理論
  • 01 Apr. 2018 - 31 Mar. 2019, 小原まり子, 日本, 東北大学大学院理学研究科博士課程, 代数的K理論
  • 01 Apr. 2021 - 31 Mar. 2022, 阿部翠空星, 日本, 埼玉大学大学院理工学研究科博士課程, 結び目理論
  • 01 Apr. 2022 - 31 Mar. 2023, 阿部翠空星, 日本, 埼玉大学大学院理工学研究科博士課程, 結び目理論