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Watanabe, Tadayuki
Graduate School of Science, Division of Mathematics and Mathematical Sciences Associate Professor
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Last Updated :2025/05/30
Basic Information
Faculty
Professional Memberships
Academic Degree
Research History
- From Apr. 2021, To PresentKyoto University, Graduate School of Science, 准教授
- From Apr. 2013, To Mar. 2021Shimane University, Interdisciplinary Faculty of Science and Engineering, Department of Mathematics and Computer Science, 講師
- From Apr. 2009, To Mar. 2013北海道大学 理学(系)研究科(研究院), 助教
- From Apr. 2008, To Mar. 2009日本学術振興会 特別研究員(PD) (受入機関：東京大学 大学院数理科学研究科)
- From Apr. 2007, To Mar. 2008京都大学数理解析研究所 研究機関研究員
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Last Updated :2025/05/30
Research
Research Topics, Overview of the research
Research Topics
Differential TopologyOverview of the research
I am working on topology of manifolds, knots, diffeomorphism groups, spaces of embeddings by means of topological invariants and surgery.
Research Interests
Research Areas
Papers
- Families of diffeomorphisms and concordances detected by trivalent graphsBoris Botvinnik; Tadayuki WatanabeJournal of Topology, 14 Feb. 2023, Peer-reviewed
- Corrigendum: On Kontsevich's characteristic classes for higher‐dimensional sphere bundles II: Higher classesTadayuki WatanabeJournal of Topology, Mar. 2022, Peer-reviewed
- Higher order generalization of Fukaya’s Morse homotopy invariant of $3$-manifolds, I: invariants of homology $3$-spheresTadayuki WatanabeAsian Journal of Mathematics, May 2018, Peer-reviewed
- 1-loop graphs and configuration space integral for embedding spacesKeiichi Sakai; Tadayuki WatanabeMATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, May 2012, Peer-reviewed
- On Kontsevich's characteristic classes for higher dimensional sphere bundles I: the simplest classTadayuki WatanabeMATHEMATISCHE ZEITSCHRIFT, Jul. 2009, Peer-reviewed
- On Kontsevich's characteristic classes for higher-dimensional sphere bundles II: Higher classesTadayuki WatanabeJOURNAL OF TOPOLOGY, 2009, Peer-reviewed
- Knotted trivalent graphs and construction of the LMO invariant from triangulationsTadayuki WatanabeOSAKA JOURNAL OF MATHEMATICS, Jun. 2007, Peer-reviewed
- Configuration space integral for longn–knots and the Alexander polynomialTadayuki WatanabeAlgebraic & Geometric Topology, 23 Feb. 2007, Peer-reviewed
- Clasper-moves among ribbon 2-knots characterizing their finite type invariantsTadayuki WatanabeJOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, Nov. 2006, Peer-reviewed
Presentations
- Theta-graph surgery for diffeomorphisms of 4-manifoldsTadayuki WatanabeInteractions of 3- and 4-dimensional topology (online), 10 Mar. 2023, Invited
- Recent results: Configuration space integral invariants / Problems (one part of Mini-Series C: diffeomorphism groups)Tadayuki WatanabeBIRS Workshop: Topology in Dimension 4.5, 03 Nov. 2022, Invited
- Theta-graph and diffeomorphisms of some 4-manifoldsTadayuki WatanabeLow-Dimensional Topology & Homeomorphism Groups (Brin Mathematics Research Center, University of Maryland), 08 Sep. 2022, Invited
- Pseudo-isotopies of some spherical 3-manifoldsTadayuki WatanabeNew Developments in Four Dimensions (University of Victoria), 15 Jun. 2022, Invited
- Families of diffeomorphisms of some 4-manifolds constructed by graphsTadayuki WatanabeThe 6th China-Japan Geometry Conference, 26 Dec. 2021, Invited
- 4次元球面の微分同相群渡邉忠之大阪大学数学教室談話会, 08 Nov. 2021, Invited
- Claspers and barbells in 4-manifoldsTadayuki Watanabe2021 Georgia Topology Conference, 08 Jun. 2021, Invited
- Theta graph and diffeomorphisms of some 4-manifolds渡邉忠之微分トポロジーセミナー (京都大学数学教室), 01 Jun. 2021, Invited
- Trivalent graphs and diffeomorphisms of some 4-manifoldsTadayuki WatanabeIntelligence of Low-dimensional Topology, 21 May 2021, Invited
- Trivalent graphs and diffeomorphisms of some 4-manifoldsTadayuki WatanabeGauge Theory Virtual, 23 Feb. 2021, Invited
- Trivalent graphs and diffeomorphisms of disksTadayuki WatanabeAlgebraic Topology Seminar (Princeton), 18 Feb. 2021, Invited
- Result in dimension 4Tadayuki WatanabeSeminar "Configuration space integrals and diffeomorphisms" (Münster), 05 Feb. 2021, Invited
- Theta-graph and 4-dimensional light bulb problem渡邉忠之微分トポロジー20, 03 Sep. 2020, Invited
- Theta-graph and diffeomorphisms of some 4-manifolds渡邉忠之ハンドルセミナー'20, 25 Jun. 2020, Invited
- Families of diffeomorphisms of 4-manifolds via graph surgery IITadayuki WatanabeSymplectic Geometry Seminar (Stanford University), 12 Nov. 2019, Invited
- Families of diffeomorphisms of 4-manifolds via graph surgery ITadayuki WatanabeSymplectic Geometry Seminar (Stanford University), 11 Nov. 2019, Invited
- Families of diffeomorphisms of 4-manifolds via graph surgeryTadayuki WatanabeWorkshop on 4-manifolds (Max Planck Institute for Mathematics, Bonn), 18 Sep. 2019, Invited
- Talk IV: Computation of the invariantTadayuki WatanabeHCM Workshop: Automorphisms of Manifolds (Lipschitz lecture hall, Mathematics Center, Bonn), 06 Sep. 2019, Invited
- Talk III: Graph surgery construction of 4-manifold bundlesTadayuki WatanabeHCM Workshop: Automorphisms of Manifolds (Lipschitz lecture hall, Mathematics Center, Bonn), 05 Sep. 2019, Invited
- Talk II: Morse theoretic propagator and graph counting formulaTadayuki WatanabeHCM Workshop: Automorphisms of Manifolds (Lipschitz lecture hall, Mathematics Center, Bonn), 03 Sep. 2019, Invited
- Talk I: Kontsevich's characteristic classesTadayuki WatanabeHCM Workshop: Automorphisms of Manifolds (Lipschitz lecture hall, Mathematics Center, Bonn), 02 Sep. 2019, Invited
- Families of diffeomorphisms of 4-manifolds via graph surgeryTadayuki WatanabeFour manifolds: Confluence of high and low dimensions (The Fields Institute, Toronto), 08 Jul. 2019, Invited
- Some exotic nontrivial elements of the rational homotopy groups of Diff(S^4)Tadayuki Watanabe微分トポロジーセミナー (京都大学数学教室), 21 May 2019, Invited
- On a 4D analogue of simultaneous normalization of propagators and its applicationsTadayuki WatanabeSeminaire de topologie (Institut Fourier, Universite Grenoble Alpes), 13 May 2019, Invited
- Kontsevich's characteristic classes and diffeomorphisms of the 4-sphere IITadayuki WatanabeSeminaire de topologie, geometrie et algebre (Laboratory of Mathematics Jean Leray, University of Sciences in Nantes), 09 May 2019, Invited
- Kontsevich's characteristic classes and diffeomorphisms of the 4-sphere ITadayuki WatanabeSeminaire de topologie, geometrie et algebre (Laboratory of Mathematics Jean Leray;University of Sciences in Nantes), 02 May 2019, Invited
- 4次元球面束のKontsevich特性類の計算渡邉忠之ENCOUNTER with MATHEMATICS (中央大学理工学部), 16 Mar. 2019, Invited
- グラフクラスパーと4次元球面束渡邉忠之ENCOUNTER with MATHEMATICS (中央大学理工学部), 16 Mar. 2019, Invited
- 4次元球面の微分同相群渡邉忠之ENCOUNTER with MATHEMATICS (中央大学理工学部), 16 Mar. 2019, Invited
- Some exotic nontrivial elements of the rational homotopy groups of Diff(S^4) (2)Tadayuki WatanabeBranched Coverings, Degenerations, and Related Topics 2019 (広島大学東広島キャンパス), 08 Mar. 2019, Invited
- Some exotic nontrivial elements of the rational homotopy groups of Diff(S^4) (1)Tadayuki WatanabeBranched Coverings, Degenerations, and Related Topics 2019 (広島大学東広島キャンパス), 07 Mar. 2019, Invited
- Some exotic nontrivial elements of the rational homotopy groups of Diff(S^4)Tadayuki WatanabeOIST Geometry, Topology and Dynamics Seminar (沖縄科学技術大学院大学(OIST)), 24 Jan. 2019, Invited
- Diff(S^4)の特性類と族のクラスパー手術渡邉忠之日本数学会2018年度秋季総合分科会（特別講演） (岡山大学津島キャンパス), 24 Sep. 2018, Invited
- 4次元Smale予想について (2)渡邉忠之種々の幾何学的構造と基本群に現れる様々な特性類とその不変量への応用 (国家公務員共済組合連合会 下呂保養所), 05 Aug. 2018, Invited
- 4次元Smale予想について (1)渡邉忠之種々の幾何学的構造と基本群に現れる様々な特性類とその不変量への応用 (国家公務員共済組合連合会 下呂保養所), 04 Aug. 2018, Invited
- Kontsevich's characteristic classes for Diff(S^4)Tadayuki Watanabe信州トポロジーセミナー (信州大学理学部数学科（松本キャンパス）), 19 Feb. 2018, Invited
- On the 4-dimensional smooth Smale conjecture渡邉忠之トポロジーとコンピュータ 2017 (大阪大学豊中キャンパス), 21 Oct. 2017, Invited
- Garoufalidis-Levine's finite type invariants for Z\pi-homology equivalences of 3-manifolds渡邉忠之Casson不変量に関わる3次元多様体の不変量 (京都大学数理解析研究所), 27 Jan. 2017, Invited
- Morse homotopy and A_infinity structures for surface bundles over S^1Tadayuki WatanabeWorkshop on finite type invariants of 3-manifolds (東京大学大学院数理科学研究科), 31 Mar. 2016, Invited
- Finite type invariants of nullhomologous knots in 3-manifolds by counting graphs渡邉忠之信州トポロジーセミナー (信州大学理学部数学科（松本キャンパス）), 15 Mar. 2016, Invited
- An invariant of fiberwise Morse functions on surface bundle over S^1 by counting graphsTadayuki Watanabe日仏共同研究小研究集会（タイヒミュラー空間と写像類群） (東京大学大学院数理科学研究科), 19 Nov. 2015, Invited
- Finite type invariants of nullhomologous knots in 3-manifolds by counting graphsTadayuki WatanabeBraids, Configuration spaces and Quantum Topology (東京大学大学院数理科学研究科), 07 Sep. 2015, Invited
- An invariant of fiberwise Morse functions on surface bundles over S^1 by counting graphs渡邉忠之リーマン面に関連する位相幾何学 (東京大学大学院数理科学研究科), 25 Aug. 2015, Invited
- On equivariant perturbative invariants in 3-dimension by Morse theoryTadayuki WatanabeRIMS Seminar Topology, Geometry and Algebra of low-dimensional manifolds (沼津KKR), 28 May 2015, Invited
- Morse theory and Lescop's equivariant propagatorTadayuki WatanabeFloer and Novikov homology, contact topology and related topics (Kavli IPMU), 22 Apr. 2014, Invited
- Morse理論と3次元多様体の不変量渡邉忠之日本数学会秋季分科会（特別講演） (愛媛大学), 24 Sep. 2013, Invited
- Morse theory and invariants of manifoldsTadayuki WatanabeThe 6th Pacific rim conference on mathematics (札幌コンベンションセンター), 02 Jul. 2013, Invited
- Invariants of 3-manifolds via Morse homotopyTadayuki WatanabeTopology seminar (Institut Fourier, Grenoble University), Mar. 2013, Invited
External funds: Kakenhi
- Diffeomorphism group and graph homologyGrant-in-Aid for Scientific Research (C)Basic Section 11020:Geometry-relatedKyoto University渡邉 忠之From 01 Apr. 2021, To 31 Mar. 2025, Granted微分同相;グラフホモロジー;手術;ファイバー束;4次元多様体;擬アイソトピー;psc計量;配置空間;グラフクラスパー;pseudo-isotopy;グラフ;微分同相群;ホモトピー;埋め込みの空間;位相不変量
- 微分可能写像の特異点理論と部分多様体の幾何のインタフェイスGrant-in-Aid for Scientific Research (C)Basic Section 11020:Geometry-relatedSeikei University高瀬 将道From 01 Apr. 2020, To 31 Mar. 2025, Granted位相幾何学;トポロジー;微分位相幾何学;多様体
- Chern-Simons perturbation theory and its application to topologyGrant-in-Aid for Scientific Research (C)Kyoto University;Shimane UniversityTadayuki WatanabeFrom 01 Apr. 2017, To 31 Mar. 2023, Project Closed微分同相群;配置空間;グラフホモロジー;4次元多様体;有限型不変量;Morse理論;ホモトピー群;可微分多様体;配置空間積分;グラフクラスパー;微分同相;Chern-Simons摂動理論;局所系;クラスパー;有理ホモトピー群;Kontsevich特性類;擬アイソトピー;埋め込み;Morseホモトピー;幾何学
- Interface between singularity theory of mappings and knot theoryGrant-in-Aid for Scientific Research (C)Seikei UniversityMasamichi TakaseFrom 01 Apr. 2015, To 31 Mar. 2020, Project Closed中次元トポロジー;幾何学;トポロジー;微分トポロジー;多様体;写像;特異点
- Morse theory and topology of manifolds / groups of diffeomorphismsGrant-in-Aid for Young Scientists (B)Shimane UniversityTadayuki WatanabeFrom 01 Apr. 2014, To 31 Mar. 2018, Project ClosedChern-Simons摂動理論;Morse理論;有限型不変量;３次元多様体;微分同相群;有理ホモトピー群;同変不変量;ファインマンダイアグラム;位相不変量;結び目
- Asymptotic dimension, topological dimension on metric spaces and topological structures of computational modelsGrant-in-Aid for Scientific Research (C)Shimane UniversityYasunao HattoriFrom 01 Apr. 2014, To 31 Mar. 2020, Project Closedドメイン;位相;次元;計算可能性;順序構造;距離空間;位相空間;次元論;形式的球体;Sorgenfrey位相;continuous bijection;reversible space;Alexandroff space;アレクサンドロフ空間;Khalimski空間;Khalimski直線;リバーシブル空間;位相幾何学;計算モデル
- Topology related to graph complexGrant-in-Aid for Young Scientists (B)Shimane University;Hokkaido UniversityTadayuki WATANABEFrom 01 Apr. 2011, To 31 Mar. 2014, Project ClosedMorse-Novikov理論;Morse理論;Chern-Simons摂動理論;グラフ複体;3次元多様体;微分同相群;曲面束;配置空間;同変不変量;ファインマンダイアグラム;有限型不変量;Lefschetzゼータ関数;埋め込み;Morse homotopy;勾配ベクトル場;位相不変量
- Topology of the group of diffeomorphisms and the spaces of embeddings of manifoldsGrant-in-Aid for Research Activity Start-upHokkaido UniversityTadayuki WATANABEFrom 01 Apr. 2009, To 31 Mar. 2011, Project Closedファイバー束;微分同相;埋め込み;Morse;理論;代数的K理論;微分同相群;Morse理論;有理ホモトピー群;擬アイソトピー
- Coho mology of discrete groups and characteristic classes of flat bundlesGrant-in-Aid for Scientific Research (B)Hokkaido UniversityToshiyuki AKITAFrom 01 Apr. 2008, To 31 Mar. 2012, Project Closedコホモロジー;特性類;線型表現;写像類群;分岐被覆;離散群;群のコホモロジー;平坦束;Mackey 函手;トポロジー;分類空間;Mackey函手;幾何学
list
Last Updated :2025/05/30
Education
Teaching subject(s)
- From 01 Apr. 2025, To 31 Mar. 2026Seminar on Topology B0521, Fall, Graduate School of Science, 3
- From 01 Apr. 2025, To 31 Mar. 2026Seminar on Topology A0520, Spring, Graduate School of Science, 3
- From 01 Apr. 2025, To 31 Mar. 2026Seminar on Topology C0522, Spring, Graduate School of Science, 3
- From 01 Apr. 2025, To 31 Mar. 2026Seminar on Topology D0523, Fall, Graduate School of Science, 3
- From 01 Apr. 2025, To 31 Mar. 2026Linear Algebra with Exercises AN151, Spring, Institute for Liberal Arts and Sciences, 3
- From 01 Apr. 2024, To 31 Mar. 2025Linear Algebra with Exercises AN151, Spring, Institute for Liberal Arts and Sciences, 3
- From 01 Apr. 2024, To 31 Mar. 2025Calculus with Exercises AN149, Spring, Institute for Liberal Arts and Sciences, 3
- From 01 Apr. 2024, To 31 Mar. 2025Introduction to Geometry2104, Fall, Faculty of Science, 2
- From 01 Apr. 2024, To 31 Mar. 2025Exercises in Basic Geometry2105, Fall, Faculty of Science, 2
- From 01 Apr. 2024, To 31 Mar. 2025Seminar on Topology A0520, Spring, Graduate School of Science, 3
- From 01 Apr. 2024, To 31 Mar. 2025Seminar on Topology D0523, Fall, Graduate School of Science, 3
- From 01 Apr. 2024, To 31 Mar. 2025Seminar on Topology C0522, Spring, Graduate School of Science, 3
- From 01 Apr. 2024, To 31 Mar. 2025Seminar on Topology B0521, Fall, Graduate School of Science, 3
- From 01 Apr. 2023, To 31 Mar. 2024Special study course (Mathematical Science)5140, Year-long, Faculty of Science, 12
- From 01 Apr. 2023, To 31 Mar. 2024Forefront of Mathematics and Mathematical Science II4139, Fall, Faculty of Science, 2
- From 01 Apr. 2023, To 31 Mar. 2024Seminar on Topology A0520, Spring, Graduate School of Science, 3
- From 01 Apr. 2023, To 31 Mar. 2024Seminar on Topology D0523, Fall, Graduate School of Science, 3
- From 01 Apr. 2023, To 31 Mar. 2024Seminar on Topology C0522, Spring, Graduate School of Science, 3
- From 01 Apr. 2023, To 31 Mar. 2024Seminar on Topology B0521, Fall, Graduate School of Science, 3
- From 01 Apr. 2023, To 31 Mar. 2024Calculus with Exercises BN150, Fall, Institute for Liberal Arts and Sciences, 3
- From 01 Apr. 2023, To 31 Mar. 2024Linear Algebra with Exercises BN152, Fall, Institute for Liberal Arts and Sciences, 3
- From 01 Apr. 2023, To 31 Mar. 2024Linear Algebra with Exercises AN151, Spring, Institute for Liberal Arts and Sciences, 3
- From 01 Apr. 2022, To 31 Mar. 2023Calculus with Exercises BN150, Fall, Institute for Liberal Arts and Sciences, 3
- From 01 Apr. 2022, To 31 Mar. 2023Exercises in Geometry II3162, Fall, Faculty of Science, 4
- From 01 Apr. 2022, To 31 Mar. 2023Seminar on Topology c0424, Spring, Graduate School of Science, 3
- From 01 Apr. 2022, To 31 Mar. 2023Set Theory & Topology2150, Spring, Faculty of Science, 2
- From 01 Apr. 2022, To 31 Mar. 2023Advanced Calculus I - Vector CalculusN124, Spring, Institute for Liberal Arts and Sciences, 2
- From 01 Apr. 2022, To 31 Mar. 2023Seminar on Topology d0425, Fall, Graduate School of Science, 3
- From 01 Apr. 2022, To 31 Mar. 2023Seminar on Topology A0520, Spring, Graduate School of Science, 3
- From 01 Apr. 2022, To 31 Mar. 2023Exercises in Set Theory & Topology2101, Spring, Faculty of Science, 2
- From 01 Apr. 2022, To 31 Mar. 2023Seminar on Topology B0521, Fall, Graduate School of Science, 3
- From 01 Apr. 2022, To 31 Mar. 2023Seminar on Topology a0422, Spring, Graduate School of Science, 3
- From 01 Apr. 2022, To 31 Mar. 2023Seminar on Topology b0423, Fall, Graduate School of Science, 3
- From Apr. 2021, To Mar. 2022Advanced Geometry IISpring, 理学部
- From Apr. 2021, To Mar. 2022Topics in Geometry DSpring, 理学研究科
- From Apr. 2021, To Mar. 2022Calculus with Exercises BFall, 全学共通科目
- From Apr. 2021, To Mar. 2022Special study course (Mathematical Science)Year-long, 理学部
- From Apr. 2021, To Mar. 2022Linear Algebra with Exercises ASpring, 全学共通科目
- From Apr. 2021, To Mar. 2022Linear Algebra with Exercises BFall, 全学共通科目
