[{"content":"Term 3, Thu. Period 2 (co-taught) · Faculty of Science, Niigata University\nSyllabus\nTextbooks\nY. Takahashi and M. Kato (supervised by S. Koshi), \u0026ldquo;微分積分概論 [新訂版]\u0026rdquo; (in Japanese), Saiensu-sha H. Anton, \u0026ldquo;Elementary Linear Algebra\u0026rdquo; (Japanese translation by J. Yamashita, Gendai-Sugakusha) ","date":"1 octubre 2026","externalUrl":null,"permalink":"/lecture/2026w_enshu_a/","section":"Teaching","summary":"Term 3, Thu. Period 2 (co-taught) · Faculty of Science, Niigata University","title":"Exercises in Mathematics A","type":"lecture"},{"content":"Term 4, Thu. Period 2 (co-taught) · Faculty of Science, Niigata University\nSyllabus\nTextbooks\nY. Takahashi and M. Kato (supervised by S. Koshi), \u0026ldquo;微分積分概論 [新訂版]\u0026rdquo; (in Japanese), Saiensu-sha H. Anton, \u0026ldquo;Elementary Linear Algebra\u0026rdquo; (Japanese translation by J. Yamashita, Gendai-Sugakusha) ","date":"1 octubre 2026","externalUrl":null,"permalink":"/lecture/2026w_enshu_b/","section":"Teaching","summary":"Term 4, Thu. Period 2 (co-taught) · Faculty of Science, Niigata University","title":"Exercises in Mathematics B","type":"lecture"},{"content":"Term 3, Mon. Period 3 · Faculty of Science, Niigata University\nSyllabus\nTextbooks\nY. Matsumoto, \u0026ldquo;多様体の基礎\u0026rdquo; (in Japanese), University of Tokyo Press Main references\nL. W. Tu, \u0026ldquo;An Introduction to Manifolds\u0026rdquo; (Japanese translation by M. Masuda, H. Abe, and T. Horiguchi, Shokabo) Y. Matsushima, \u0026ldquo;多様体入門\u0026rdquo; (in Japanese), Shokabo Course contents\nDefinition of manifolds Examples of manifolds (on-demand lecture) $C^{\\infty}$ functions $C^{\\infty}$ maps Tangent spaces Differentials of $C^{\\infty}$ maps Examples of differentials of $C^{\\infty}$ maps Local properties of maps; exam ","date":"1 octubre 2026","externalUrl":null,"permalink":"/lecture/2026w_geometryiia/","section":"Teaching","summary":"Term 3, Mon. Period 3 · Faculty of Science, Niigata University","title":"Geometry IIA","type":"lecture"},{"content":"Term 4, Mon. Period 3 · Faculty of Science, Niigata University\nSyllabus\nTextbooks\nY. Matsumoto, \u0026ldquo;多様体の基礎\u0026rdquo; (in Japanese), University of Tokyo Press Main references\nL. W. Tu, \u0026ldquo;An Introduction to Manifolds\u0026rdquo; (Japanese translation by M. Masuda, H. Abe, and T. Horiguchi, Shokabo) Y. Matsushima, \u0026ldquo;多様体入門\u0026rdquo; (in Japanese), Shokabo Recommended reading\nR. Bott and L. W. Tu, \u0026ldquo;Differential Forms in Algebraic Topology\u0026rdquo; (Japanese translation by M. Mimura, Maruzen) Course contents\nImmersions and embeddings The embedding theorem; regular and critical points, part 1 Regular and critical points, part 2 Vector fields, part 1 Vector fields, part 2 Differential forms, part 1 Differential forms, part 2 Differential forms, part 3; exam ","date":"1 octubre 2026","externalUrl":null,"permalink":"/lecture/2026w_geometryiib/","section":"Teaching","summary":"Term 4, Mon. Period 3 · Faculty of Science, Niigata University","title":"Geometry IIB","type":"lecture"},{"content":"","date":"1 octubre 2026","externalUrl":null,"permalink":"/lecture/","section":"Teaching","summary":"","title":"Teaching","type":"lecture"},{"content":"For master\u0026rsquo;s students; Semester 2, Thu. Period 3 · Graduate School of Integrated Studies and Graduate School of Science and Technology, Niigata University\nSyllabus\n","date":"1 octubre 2026","externalUrl":null,"permalink":"/lecture/2026w_difftopom/","section":"Teaching","summary":"For master’s students; Semester 2, Thu. Period 3 · Graduate School of Integrated Studies and Graduate School of Science and Technology, Niigata University","title":"Topics in Differential Topology","type":"lecture"},{"content":" Ryuma Orita\narXiv:2607.20886\nAbstract # We continue the study of Farber\u0026rsquo;s topological complexity for monotone symplectic manifolds initiated in [Or25]. First, we show that a closed spherically monotone symplectic manifold whose fundamental group contains no subgroup isomorphic to $\\mathbb{Z}\\oplus\\mathbb{Z}$ is automatically toroidally monotone, with the same monotonicity constant. As a consequence, every closed $4$-dimensional spherically monotone symplectic manifold whose Kodaira dimension is not $-\\infty$ and whose fundamental group contains no $\\mathbb{Z}\\oplus\\mathbb{Z}$ (for instance, is Gromov hyperbolic) has maximal topological complexity $\\mathrm{TC}(M)=9$. This settles, under strictly weaker hypotheses, the dichotomy $\\mathrm{TC}(M)=8$, $9$ left open there. Second, we compute the topological complexity and the Lusternik\u0026ndash;Schnirelmann category of all blowups of $S^2$-bundles over closed orientable surfaces of genus $g\\geq 2$: they satisfy $\\mathrm{cat}(M)=4$ and $\\mathrm{TC}(M)=7$. In particular, the hypothesis on the Kodaira dimension in the first result cannot be removed, and closed symplectic $4$-manifolds realize the pairs $(\\mathrm{cat}(M),\\mathrm{TC}(M))=(3,5)$, $(4,7)$, $(5,9)$ in the three regimes considered in this paper. Throughout, $\\mathrm{TC}$ and $\\mathrm{cat}$ are taken in the unreduced convention.\n","date":"23 julio 2026","externalUrl":null,"permalink":"/publication/14-tc2/","section":"Publications","summary":"Ryuma Orita — arXiv:2607.20886","title":"Maximal topological complexity of monotone symplectic 4-manifolds","type":"publication"},{"content":"","date":"23 julio 2026","externalUrl":null,"permalink":"/publication/","section":"Publications","summary":"","title":"Publications","type":"publication"},{"content":" Morimichi Kawasaki, Mitsuaki Kimura, Hiroki Kodama, Yoshifumi Matsuda, Takahiro Matsushita, Ryuma Orita\nJournal of Topology and Analysis, Online Ready\n· Abstract # Many transformation groups on manifolds are simple, but their universal coverings are not. In the present paper, we study the concept of relatively simple group, that is, a group with the maximum proper normal subgroup. We show that many examples of universal coverings of transformation groups are relatively simple, including the universal covering $\\widetilde{\\mathrm{Ham}}(M,\\omega)$ of the group of Hamiltonian diffeomorphisms of a closed symplectic manifold $(M,\\omega)$. Tsuboi constructed a metric space $\\mathcal{M}(G)$ for a simple group $G$. We generalize his construction to relatively simple groups, and study their large scale geometric structure. In particular, Tsuboi\u0026rsquo;s metric space of $\\widetilde{\\mathrm{Ham}}(M,\\omega)$ is not quasi-isometric to the half line for every closed symplectic manifold $(M,\\omega)$.\n","date":"30 junio 2026","externalUrl":null,"permalink":"/publication/12-tsuboi-metric/","section":"Publications","summary":"Morimichi Kawasaki, Mitsuaki Kimura, Hiroki Kodama, Yoshifumi Matsuda, Takahiro Matsushita, Ryuma Orita — Journal of Topology and Analysis, Online Ready","title":"Relative simplicity of the universal coverings of transformation groups and Tsuboi's metric","type":"publication"},{"content":"Osaka-Tsukuba Online Workshop on Complex Geometry and Dynamics\nOnline (Zoom)\n","date":"12 junio 2026","externalUrl":null,"permalink":"/talk/2026-06-osakatsukuba/","section":"Talks","summary":"Osaka-Tsukuba Online Workshop on Complex Geometry and Dynamics · Online (Zoom)","title":"Morse-Bott-Smale chain complex","type":"talk"},{"content":"","date":"12 junio 2026","externalUrl":null,"permalink":"/talk/","section":"Talks","summary":"","title":"Talks","type":"talk"},{"content":"Shinshu Topology Seminar\nShinshu University, Japan\n","date":"14 mayo 2026","externalUrl":null,"permalink":"/talk/2026-05-shinshuu/","section":"Talks","summary":"Shinshu Topology Seminar · Shinshu University, Japan","title":"Morse-Bott-Smale chain complex","type":"talk"},{"content":"For doctoral students; Semester 1, Thu. Period 3 · Graduate School of Science and Technology, Niigata University\nSyllabus\nTextbooks\nM. Audin and M. Damian, \u0026ldquo;Morse Theory and Floer Homology\u0026rdquo;, Springer Course contents\nThe Arzelà\u0026ndash;Ascoli theorem Fredholm theory Distribution spaces and weak solutions Sobolev spaces on $\\mathbb{R}^n$ The Cauchy\u0026ndash;Riemann equation The Banach manifold $\\mathcal{P}^{1,p}(x,y)$ ","date":"1 abril 2026","externalUrl":null,"permalink":"/lecture/2026s_difftopod/","section":"Teaching","summary":"For doctoral students; Semester 1, Thu. Period 3 · Graduate School of Science and Technology, Niigata University","title":"Differential Topology","type":"lecture"},{"content":"Term 1, Mon. Period 3 \u0026amp; Tue. Period 2 · Faculty of Science, Niigata University\nSyllabus\nTextbooks\nM. Umehara and K. Yamada, \u0026ldquo;曲線と曲面（改訂版）\u0026rdquo; (in Japanese), Shokabo Main references\nS. Kobayashi, \u0026ldquo;曲線と曲面の微分幾何（改訂版）\u0026rdquo; (in Japanese), Shokabo Recommended reading\nManfredo P. do Carmo, Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition, Dover Publications ","date":"1 abril 2026","externalUrl":null,"permalink":"/lecture/2026s_geometryia/","section":"Teaching","summary":"Term 1, Mon. Period 3 \u0026 Tue. Period 2 · Faculty of Science, Niigata University","title":"Geometry IA","type":"lecture"},{"content":"Term 2, Mon. Period 3 \u0026amp; Tue. Period 2 · Faculty of Science, Niigata University\nSyllabus\nTextbooks\nK. Komiya, \u0026ldquo;位相幾何入門\u0026rdquo; (in Japanese), Shokabo Main references\nI. Tamura, \u0026ldquo;トポロジー\u0026rdquo; (in Japanese), Iwanami Zensho Recommended reading\nY. Hiraoka, \u0026ldquo;タンパク質構造とトポロジー\u0026rdquo; (in Japanese), Kyoritsu Shuppan ","date":"1 abril 2026","externalUrl":null,"permalink":"/lecture/2026s_geometryib/","section":"Teaching","summary":"Term 2, Mon. Period 3 \u0026 Tue. Period 2 · Faculty of Science, Niigata University","title":"Geometry IB","type":"lecture"},{"content":"Intensive course (co-taught) · Faculty of Science, Niigata University\nSyllabus\nCourse contents (Orita\u0026rsquo;s part)\nDifferential geometry of curves and road design Topological data analysis ","date":"1 abril 2026","externalUrl":null,"permalink":"/lecture/2026s_kagakutoshakai/","section":"Teaching","summary":"Intensive course (co-taught) · Faculty of Science, Niigata University","title":"Science and Society","type":"lecture"},{"content":"Terms 1–2, Wed. Period 3 (co-taught) · Faculty of Science, Niigata University\nSyllabus\nCourse contents (Orita\u0026rsquo;s part)\nDifferential geometry of curves and road design (4/22) Topological data analysis (4/27) ","date":"1 abril 2026","externalUrl":null,"permalink":"/lecture/2026s_kagakugijutsutoshakai/","section":"Teaching","summary":"Terms 1–2, Wed. Period 3 (co-taught) · Faculty of Science, Niigata University","title":"Science, Technology and Society","type":"lecture"},{"content":"Term 4, Mon. Period 3 · Faculty of Science, Niigata University\nSyllabus\nTextbooks\nY. Matsumoto, \u0026ldquo;多様体の基礎\u0026rdquo; (in Japanese), University of Tokyo Press Main references\nL. W. Tu, \u0026ldquo;An Introduction to Manifolds\u0026rdquo; (Japanese translation by M. Masuda, H. Abe, and T. Horiguchi, Shokabo) Y. Matsushima, \u0026ldquo;多様体入門\u0026rdquo; (in Japanese), Shokabo Recommended reading\nR. Bott and L. W. Tu, \u0026ldquo;Differential Forms in Algebraic Topology\u0026rdquo; (Japanese translation by M. Mimura, Maruzen) Course contents\nImmersions and embeddings The embedding theorem; regular and critical points, part 1 Regular and critical points, part 2 Vector fields, part 1 Vector fields, part 2 Differential forms, part 1 Differential forms, part 2 Differential forms, part 3; exam ","date":"8 diciembre 2025","externalUrl":null,"permalink":"/lecture/2025w_geometryiib/","section":"Teaching","summary":"Term 4, Mon. Period 3 · Faculty of Science, Niigata University","title":"Geometry IIB","type":"lecture"},{"content":"Term 4, Thu. Period 2 (co-taught) · Faculty of Science, Niigata University\nSyllabus\nTextbooks\nY. Takahashi and M. Kato (supervised by S. Koshi), \u0026ldquo;微分積分概論 [新訂版]\u0026rdquo; (in Japanese), Saiensu-sha H. Anton, \u0026ldquo;Elementary Linear Algebra\u0026rdquo; (Japanese translation by J. Yamashita, Gendai-Sugakusha) ","date":"4 diciembre 2025","externalUrl":null,"permalink":"/lecture/2025w_enshu_b/","section":"Teaching","summary":"Term 4, Thu. Period 2 (co-taught) · Faculty of Science, Niigata University","title":"Exercises in Mathematics B","type":"lecture"},{"content":"The 2nd Niigata Young Algebra and Geometry Symposium\nNiigata University, Japan\n","date":"28 noviembre 2025","externalUrl":null,"permalink":"/talk/2025-11-niigatau/","section":"Talks","summary":"The 2nd Niigata Young Algebra and Geometry Symposium · Niigata University, Japan","title":"Morse-Bott-Smale chain complex","type":"talk"},{"content":"Term 3, Mon. Period 3 · Faculty of Science, Niigata University\nSyllabus\nTextbooks\nY. Matsumoto, \u0026ldquo;多様体の基礎\u0026rdquo; (in Japanese), University of Tokyo Press Main references\nL. W. Tu, \u0026ldquo;An Introduction to Manifolds\u0026rdquo; (Japanese translation by M. Masuda, H. Abe, and T. Horiguchi, Shokabo) Y. Matsushima, \u0026ldquo;多様体入門\u0026rdquo; (in Japanese), Shokabo Course contents\nDefinition of manifolds Examples of manifolds (on-demand lecture) $C^{\\infty}$ functions $C^{\\infty}$ maps Tangent spaces Differentials of $C^{\\infty}$ maps Examples of differentials of $C^{\\infty}$ maps Local properties of maps; exam ","date":"6 octubre 2025","externalUrl":null,"permalink":"/lecture/2025w_geometryiia/","section":"Teaching","summary":"Term 3, Mon. Period 3 · Faculty of Science, Niigata University","title":"Geometry IIA","type":"lecture"},{"content":"Term 3, Thu. Period 2 (co-taught) · Faculty of Science, Niigata University\nSyllabus\nTextbooks\nY. Takahashi and M. Kato (supervised by S. Koshi), \u0026ldquo;微分積分概論 [新訂版]\u0026rdquo; (in Japanese), Saiensu-sha H. Anton, \u0026ldquo;Elementary Linear Algebra\u0026rdquo; (Japanese translation by J. Yamashita, Gendai-Sugakusha) ","date":"2 octubre 2025","externalUrl":null,"permalink":"/lecture/2025w_enshu_a/","section":"Teaching","summary":"Term 3, Thu. Period 2 (co-taught) · Faculty of Science, Niigata University","title":"Exercises in Mathematics A","type":"lecture"},{"content":"For doctoral students; Semester 2, intensive course · Graduate School of Science and Technology, Niigata University\nSyllabus\nNote\nThis course is planned as an intensive course.\nTextbooks\nJohn W. Milnor, \u0026ldquo;Morse Theory\u0026rdquo;, Princeton University Press Course contents\nReview of Morse theory on path spaces (Part III) Symmetric spaces (§20) Lie groups as symmetric spaces (§21) Manifolds of minimal geodesics (§22) The Bott periodicity theorem for the unitary group (§23) The Bott periodicity theorem for the orthogonal group (§24) ","date":"1 octubre 2025","externalUrl":null,"permalink":"/lecture/2025w_difftopod/","section":"Teaching","summary":"For doctoral students; Semester 2, intensive course · Graduate School of Science and Technology, Niigata University","title":"Differential Topology","type":"lecture"},{"content":"Intensive course (co-taught) · Faculty of Science, Niigata University\nSyllabus\nCourse contents (Orita\u0026rsquo;s part)\nDifferential geometry of curves and road design Topological data analysis ","date":"21 agosto 2025","externalUrl":null,"permalink":"/lecture/2025s_kagakutoshakai/","section":"Teaching","summary":"Intensive course (co-taught) · Faculty of Science, Niigata University","title":"Science and Society","type":"lecture"},{"content":"Semester 1 intensive course by Prof. Yuichi Ike (The University of Tokyo) · Graduate School of Science and Technology, Niigata University\nSyllabus\nCourse contents\nSessions 1–4: operations on sheaves Sessions 5–8: the derived category of sheaves, Grothendieck\u0026rsquo;s six operations, and applications ","date":"22 julio 2025","externalUrl":null,"permalink":"/lecture/2025s_sentansouron/","section":"Teaching","summary":"Semester 1 intensive course by Prof. Yuichi Ike (The University of Tokyo) · Graduate School of Science and Technology, Niigata University","title":"Overview of Advanced Science and Technology","type":"lecture"},{"content":"Term 2, Mon. Period 3 \u0026amp; Tue. Period 2 · Faculty of Science, Niigata University\nSyllabus\nTextbooks\nK. Komiya, \u0026ldquo;位相幾何入門\u0026rdquo; (in Japanese), Shokabo Main references\nI. Tamura, \u0026ldquo;トポロジー\u0026rdquo; (in Japanese), Iwanami Zensho Recommended reading\nY. Hiraoka, \u0026ldquo;タンパク質構造とトポロジー\u0026rdquo; (in Japanese), Kyoritsu Shuppan ","date":"9 junio 2025","externalUrl":null,"permalink":"/lecture/2025s_geometryib/","section":"Teaching","summary":"Term 2, Mon. Period 3 \u0026 Tue. Period 2 · Faculty of Science, Niigata University","title":"Geometry IB","type":"lecture"},{"content":"Ryuma Orita, Kanon Yashiro\narXiv:2504.16962\nAbstract # Banyaga and Hurtubise defined the Morse\u0026ndash;Bott\u0026ndash;Smale chain complex as a quotient of a large chain complex by introducing five degeneracy relations. However, their five degeneracy relations are in fact redundant. In the present paper, we unify these five conditions into a single degeneracy condition and resolve the issue of the well-definedness of the Morse\u0026ndash;Bott\u0026ndash;Smale chain complex. This provides an appropriate definition of the Morse\u0026ndash;Bott homology and more computable examples. Moreover, we show that our chain complex for a Morse\u0026ndash;Smale function is quasi-isomorphic to the usual Morse\u0026ndash;Smale\u0026ndash;Witten chain complex. As a consequence, we obtain an alternative proof of the Morse Homology Theorem.\n","date":"23 abril 2025","externalUrl":null,"permalink":"/publication/13-morse-bott-homology/","section":"Publications","summary":"Ryuma Orita, Kanon Yashiro — arXiv:2504.16962","title":"Morse-Bott-Smale chain complex","type":"publication"},{"content":"For master\u0026rsquo;s students; Semester 1, Thu. Period 3 (irregular) · Graduate School of Science and Technology, Niigata University\nSyllabus\nNote\nHeld irregularly on Thu. Period 3; the first session is on 4/10.\nSchedule (as of 2025-07-10)\nManifolds, tangent spaces, and differentials (4/10) Vector fields and differential forms (4/24) Pullbacks, wedge products, and exterior derivatives (5/8) Definition of symplectic manifolds (5/15) Examples of symplectic manifolds (5/29) Cotangent bundles (6/12) Lie derivatives, interior products, and Cartan\u0026rsquo;s formula (7/10) Hamiltonian dynamics 1 (8/6) Hamiltonian dynamics 2 (8/6) Hamiltonian dynamics 3 (8/7) Hamiltonian dynamics 4 (8/7) ","date":"10 abril 2025","externalUrl":null,"permalink":"/lecture/2025s_difftopom/","section":"Teaching","summary":"For master’s students; Semester 1, Thu. Period 3 (irregular) · Graduate School of Science and Technology, Niigata University","title":"Topics in Differential Topology","type":"lecture"},{"content":"Terms 1–2, Wed. Period 3 (co-taught) · Faculty of Science, Niigata University\nSyllabus\nCourse contents (Orita\u0026rsquo;s part)\nDifferential geometry of curves and road design (4/23) Topological data analysis (4/30) ","date":"9 abril 2025","externalUrl":null,"permalink":"/lecture/2025s_kagakugijutsutoshakai/","section":"Teaching","summary":"Terms 1–2, Wed. Period 3 (co-taught) · Faculty of Science, Niigata University","title":"Science, Technology and Society","type":"lecture"},{"content":"Term 1, Mon. Period 3 \u0026amp; Tue. Period 2 · Faculty of Science, Niigata University\nSyllabus\nNote\nNo class on Tue. 4/8; the first session is on Mon. 4/14.\n","date":"8 abril 2025","externalUrl":null,"permalink":"/lecture/2025s_geometryia/","section":"Teaching","summary":"Term 1, Mon. Period 3 \u0026 Tue. Period 2 · Faculty of Science, Niigata University","title":"Geometry IA","type":"lecture"},{"content":"D2: 1, D1: 1, M2: 1, M1: 1, B4: 5 (AY 2025) · Faculty of Science and Graduate School of Science and Technology, Niigata University\nMembers (AY 2025) # D2 # KY: Algebraic topology and applications of Morse theory D1 # KY: Teichmüller space and the Thurston spine M2 # SY: Pseudo-Riemannian geometry and relativity M1 # CT: Morse homology B4 # JG (graduated on September 22, 2025) SF, SK, TM, SO: \u0026ldquo;位相的データ解析から構造発見へ\u0026rdquo; by Y. Ike, E. G. Escolar, I. Obayashi, and S. Kaji (in Japanese) ","date":"1 abril 2025","externalUrl":null,"permalink":"/lecture/2025_zemi/","section":"Teaching","summary":"D2: 1, D1: 1, M2: 1, M1: 1, B4: 5 (AY 2025) · Faculty of Science and Graduate School of Science and Technology, Niigata University","title":"Research Group (Seminar)","type":"lecture"},{"content":" Ryuma Orita\nTokyo Journal of Mathematics, vol. 48 (2025), no. 1, pp. 217-230\n· Abstract # We study Farber\u0026rsquo;s topological complexity for monotone symplectic manifolds. More precisely, we estimate the topological complexity of 4-dimensional spherically monotone manifolds whose Kodaira dimension is not $-\\infty$.\n","date":"21 febrero 2025","externalUrl":null,"permalink":"/publication/10-tc/","section":"Publications","summary":"Ryuma Orita — Tokyo Journal of Mathematics, vol. 48 (2025), no. 1, pp. 217-230","title":"Topological complexity of monotone symplectic manifolds","type":"publication"},{"content":"Workshop on geometry of foliations and its applications\nKyoto University of Education, Japan\n","date":"21 diciembre 2024","externalUrl":null,"permalink":"/talk/2024-12-kyokyou/","section":"Talks","summary":"Workshop on geometry of foliations and its applications · Kyoto University of Education, Japan","title":"Floer-type bipersistence modules and rectangle barcodes","type":"talk"},{"content":"Term 4, Thu. Period 2 (co-taught) · Faculty of Science, Niigata University\nSyllabus\nTextbooks\nY. Takahashi and M. Kato (supervised by S. Koshi), \u0026ldquo;微分積分概論 [新訂版]\u0026rdquo; (in Japanese), Saiensu-sha H. Anton, \u0026ldquo;Elementary Linear Algebra\u0026rdquo; (Japanese translation by J. Yamashita, Gendai-Sugakusha) ","date":"5 diciembre 2024","externalUrl":null,"permalink":"/lecture/2024w_enshu_b/","section":"Teaching","summary":"Term 4, Thu. Period 2 (co-taught) · Faculty of Science, Niigata University","title":"Exercises in Mathematics B","type":"lecture"},{"content":"Term 4, Mon. Period 3 · Faculty of Science, Niigata University\nSyllabus\nTextbooks\nY. Matsumoto, \u0026ldquo;多様体の基礎\u0026rdquo; (in Japanese), University of Tokyo Press Main references\nL. W. Tu, \u0026ldquo;An Introduction to Manifolds\u0026rdquo; (Japanese translation by M. Masuda, H. Abe, and T. Horiguchi, Shokabo) Y. Matsushima, \u0026ldquo;多様体入門\u0026rdquo; (in Japanese), Shokabo Recommended reading\nR. Bott and L. W. Tu, \u0026ldquo;Differential Forms in Algebraic Topology\u0026rdquo; (Japanese translation by M. Mimura, Maruzen) Course contents\nImmersions and embeddings The embedding theorem; regular and critical points, part 1 Regular and critical points, part 2 Vector fields, part 1 Vector fields, part 2 Differential forms, part 1 Differential forms, part 2 Differential forms, part 3 ","date":"2 diciembre 2024","externalUrl":null,"permalink":"/lecture/2024w_geometryiib/","section":"Teaching","summary":"Term 4, Mon. Period 3 · Faculty of Science, Niigata University","title":"Geometry IIB","type":"lecture"},{"content":"Term 3, Mon. Period 3 · Faculty of Science, Niigata University\nSyllabus\nTextbooks\nY. Matsumoto, \u0026ldquo;多様体の基礎\u0026rdquo; (in Japanese), University of Tokyo Press Main references\nL. W. Tu, \u0026ldquo;An Introduction to Manifolds\u0026rdquo; (Japanese translation by M. Masuda, H. Abe, and T. Horiguchi, Shokabo) Y. Matsushima, \u0026ldquo;多様体入門\u0026rdquo; (in Japanese), Shokabo Course contents\nDefinition of manifolds Examples of manifolds $C^{\\infty}$ functions $C^{\\infty}$ maps Tangent spaces Differentials of $C^{\\infty}$ maps Examples of differentials of $C^{\\infty}$ maps; local properties of maps ","date":"7 octubre 2024","externalUrl":null,"permalink":"/lecture/2024w_geometryiia/","section":"Teaching","summary":"Term 3, Mon. Period 3 · Faculty of Science, Niigata University","title":"Geometry IIA","type":"lecture"},{"content":"For doctoral students; Semester 2 · Graduate School of Science and Technology, Niigata University\nSyllabus\nNote\nThis course is planned as an intensive course.\nTextbooks\nJohn W. Milnor, \u0026ldquo;Morse Theory\u0026rdquo;, Princeton University Press Course contents\nReview of Morse theory on finite-dimensional manifolds Review of Riemannian geometry Review of Morse theory on path spaces Applications to Lie groups and symmetric spaces ","date":"3 octubre 2024","externalUrl":null,"permalink":"/lecture/2024w_difftopod/","section":"Teaching","summary":"For doctoral students; Semester 2 · Graduate School of Science and Technology, Niigata University","title":"Differential Topology","type":"lecture"},{"content":"Term 3, Thu. Period 2 (co-taught) · Faculty of Science, Niigata University\nSyllabus\nTextbooks\nY. Takahashi and M. Kato (supervised by S. Koshi), \u0026ldquo;微分積分概論 [新訂版]\u0026rdquo; (in Japanese), Saiensu-sha H. Anton, \u0026ldquo;Elementary Linear Algebra\u0026rdquo; (Japanese translation by J. Yamashita, Gendai-Sugakusha) ","date":"3 octubre 2024","externalUrl":null,"permalink":"/lecture/2024w_enshu_a/","section":"Teaching","summary":"Term 3, Thu. Period 2 (co-taught) · Faculty of Science, Niigata University","title":"Exercises in Mathematics A","type":"lecture"},{"content":"Singularity Theory and its related fields\nChitose Arcadia Plaza, Japan\n","date":"20 junio 2024","externalUrl":null,"permalink":"/talk/2024-06-chitose/","section":"Talks","summary":"Singularity Theory and its related fields · Chitose Arcadia Plaza, Japan","title":"Morse bipersistence modules and rectangle barcodes","type":"talk"},{"content":"Term 2, Mon. Period 3 \u0026amp; Tue. Period 2 · Faculty of Science, Niigata University\nSyllabus\nTextbooks\nK. Komiya, \u0026ldquo;位相幾何入門\u0026rdquo; (in Japanese), Shokabo Main references\nI. Tamura, \u0026ldquo;トポロジー\u0026rdquo; (in Japanese), Iwanami Zensho Recommended reading\nY. Hiraoka, \u0026ldquo;タンパク質構造とトポロジー\u0026rdquo; (in Japanese), Kyoritsu Shuppan Course contents\nTopological spaces Quotient spaces; closed surfaces and connected sums Classification of closed surfaces Simplices and simplicial complexes Skeletons and polyhedra; group theory, part 1 Group theory, part 2; oriented simplices Chain groups and homology groups Midterm exam Computing homology groups; simplicial maps Chain homomorphisms; homology groups of polyhedra, part 1 (definitions); homotopy Homology groups of polyhedra, part 2 (homotopy invariance) Euler numbers; homology groups and homomorphisms The Mayer-Vietoris exact sequence Homology groups of closed surfaces Persistent homology groups and protein structures End-of-term exam and summary ","date":"10 junio 2024","externalUrl":null,"permalink":"/lecture/2024s_geometryib/","section":"Teaching","summary":"Term 2, Mon. Period 3 \u0026 Tue. Period 2 · Faculty of Science, Niigata University","title":"Geometry IB","type":"lecture"},{"content":"Topology Seminar\nOsaka University, Japan\n","date":"5 junio 2024","externalUrl":null,"permalink":"/talk/2024-06-osakau/","section":"Talks","summary":"Topology Seminar · Osaka University, Japan","title":"2-parameter persistence modules and rectangle barcodes","type":"talk"},{"content":"Semester 1 intensive course by Prof. Yuichi Ike (Kyushu University) · Graduate School of Science and Technology, Niigata University\nSyllabus\nCourse contents\nSessions 1–2: sheaves and sheaf cohomology Sessions 3–6: Morse theory for sheaves Sessions 7–8: the derived category of sheaves and its applications ","date":"7 mayo 2024","externalUrl":null,"permalink":"/lecture/2024s_sentansouron/","section":"Teaching","summary":"Semester 1 intensive course by Prof. Yuichi Ike (Kyushu University) · Graduate School of Science and Technology, Niigata University","title":"Overview of Advanced Science and Technology","type":"lecture"},{"content":"For master\u0026rsquo;s students; Semester 1 · Graduate School of Science and Technology, Niigata University\nSyllabus\nNote\nThis course is planned as an intensive course.\nTextbooks\nCourse contents\n","date":"11 abril 2024","externalUrl":null,"permalink":"/lecture/2024s_difftopom/","section":"Teaching","summary":"For master’s students; Semester 1 · Graduate School of Science and Technology, Niigata University","title":"Topics in Differential Topology","type":"lecture"},{"content":"Terms 1–2, Wed. Period 3 (co-taught) · Faculty of Science, Niigata University\nSyllabus\nCourse contents (Orita\u0026rsquo;s part)\nDifferential geometry of curves and road design (4/10) Topological data analysis (5/22) ","date":"10 abril 2024","externalUrl":null,"permalink":"/lecture/2024s_kagakugijutsutoshakai/","section":"Teaching","summary":"Terms 1–2, Wed. Period 3 (co-taught) · Faculty of Science, Niigata University","title":"Science, Technology and Society","type":"lecture"},{"content":"Term 1, Mon. Period 3 \u0026amp; Tue. Period 2 · Faculty of Science, Niigata University\nSyllabus\nTextbooks\nM. Umehara and K. Yamada, \u0026ldquo;曲線と曲面（改訂版）\u0026rdquo; (in Japanese), Shokabo Main references\nS. Kobayashi, \u0026ldquo;曲線と曲面の微分幾何（改訂版）\u0026rdquo; (in Japanese), Shokabo Recommended reading\nManfredo P. do Carmo, Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition, Dover Publications Course contents\nWhat is a curve? Curvature The Frenet formulas The fundamental theorem of plane curves; the four-vertex theorem Space curves Midterm exam What is a surface? The first fundamental form, part 1 (definition) The first fundamental form, part 2 (areas and lengths) The first fundamental form, part 3 (angles, maps); the second fundamental form, part 1 (definition) The second fundamental form, part 2 (curvatures, invariance) The second fundamental form, part 3 (the Weingarten formulas); definition of normal curvature Normal and principal curvatures; geodesics Theorema Egregium; the Gauss-Bonnet theorem End-of-term exam and summary ","date":"8 abril 2024","externalUrl":null,"permalink":"/lecture/2024s_geometryia/","section":"Teaching","summary":"Term 1, Mon. Period 3 \u0026 Tue. Period 2 · Faculty of Science, Niigata University","title":"Geometry IA","type":"lecture"},{"content":"D1: 1, M2: 1, M1: 1, B4: 4 (AY 2024) · Faculty of Science and Graduate School of Science and Technology, Niigata University\nMembers (AY 2024) # D1 # KY: Algebraic topology and applications of Morse theory M2 # KY: Teichmüller space and the Thurston spine M1 # SY: Pseudo-Riemannian geometry and relativity B4 # JG, KS: \u0026ldquo;An Introduction to Algebraic Topology\u0026rdquo; by Joseph J. Rotman CT: \u0026ldquo;Morse Theory\u0026rdquo; by John W. Milnor RK: \u0026ldquo;位相的データ解析から構造発見へ\u0026rdquo; by Y. Ike, E. G. Escolar, I. Obayashi, and S. Kaji (in Japanese) ","date":"1 abril 2024","externalUrl":null,"permalink":"/lecture/2024_zemi/","section":"Teaching","summary":"D1: 1, M2: 1, M1: 1, B4: 4 (AY 2024) · Faculty of Science and Graduate School of Science and Technology, Niigata University","title":"Research Group (Seminar)","type":"lecture"},{"content":"AATRN Topological Complexity Seminar\nZoom\nAbstract # In this talk I will estimate the topological complexity of 4-dimensional spherically monotone manifolds whose Kodaira dimension is not negative infinity.\n","date":"23 febrero 2024","externalUrl":null,"permalink":"/talk/2024-02-aatrn-tc/","section":"Talks","summary":"AATRN Topological Complexity Seminar · Zoom","title":"Topological complexity of monotone symplectic manifolds","type":"talk"},{"content":" Kanta Koeda, Ryuma Orita, Kanon Yashiro\narXiv:2312.07847\nAbstract # In this paper, we show that the pointwise finite-dimensional two-parameter persistence module $\\mathbb{HF}_{\\ast}^{(\\bullet,\\bullet]}$, defined in terms of interlevel filtered Floer homology, is rectangle-decomposable. This allows for the definition of a barcode consisting only of rectangles in $\\mathbb{R}^2$ associated with the bipersistence module. We observe that this rectangle barcode contains information about Usher\u0026rsquo;s boundary depth and spectral invariants developed by Oh, Schwarz, and Viterbo. Moreover, we introduce a novel invariant extracted from the rectangle barcode, which proves instrumental in detecting periodic solutions of Hamiltonian systems. Additionally, we establish relevant stability results, particularly concerning the bottleneck distance and Hofer\u0026rsquo;s distance.\n","date":"13 diciembre 2023","externalUrl":null,"permalink":"/publication/11-floer-type-bipersistence-modules/","section":"Publications","summary":"Kanta Koeda, Ryuma Orita, Kanon Yashiro — arXiv:2312.07847","title":"Floer-type bipersistence modules and rectangle barcodes","type":"publication"},{"content":"Term 4, Mon. Period 3 · Faculty of Science, Niigata University\nSyllabus\nTextbooks\nY. Matsumoto, \u0026ldquo;多様体の基礎\u0026rdquo; (in Japanese), University of Tokyo Press Main references\nL. W. Tu, \u0026ldquo;An Introduction to Manifolds\u0026rdquo; (Japanese translation by M. Masuda, H. Abe, and T. Horiguchi, Shokabo) Y. Matsushima, \u0026ldquo;多様体入門\u0026rdquo; (in Japanese), Shokabo Recommended reading\nR. Bott and L. W. Tu, \u0026ldquo;Differential Forms in Algebraic Topology\u0026rdquo; (Japanese translation by M. Mimura, Maruzen) Course contents\nImmersions and embeddings The embedding theorem; regular and critical points, part 1 Regular and critical points, part 2 Vector fields, part 1 Vector fields, part 2 Differential forms, part 1 Differential forms, part 2 Differential forms, part 3 ","date":"4 diciembre 2023","externalUrl":null,"permalink":"/lecture/2023w_geometryiib/","section":"Teaching","summary":"Term 4, Mon. Period 3 · Faculty of Science, Niigata University","title":"Geometry IIB","type":"lecture"},{"content":"The 7th Workshop on Geometric Group Theory\nNiigata Unison Plaza, Japan\n","date":"27 noviembre 2023","externalUrl":null,"permalink":"/talk/2023-11-ggt/","section":"Talks","summary":"The 7th Workshop on Geometric Group Theory · Niigata Unison Plaza, Japan","title":"Topological complexity of monotone symplectic manifolds","type":"talk"},{"content":"Term 3, Mon. Period 3 · Faculty of Science, Niigata University\nSyllabus\nTextbooks\nY. Matsumoto, \u0026ldquo;多様体の基礎\u0026rdquo; (in Japanese), University of Tokyo Press Main references\nL. W. Tu, \u0026ldquo;An Introduction to Manifolds\u0026rdquo; (Japanese translation by M. Masuda, H. Abe, and T. Horiguchi, Shokabo) Y. Matsushima, \u0026ldquo;多様体入門\u0026rdquo; (in Japanese), Shokabo Course contents\nDefinition of manifolds Examples of manifolds $C^{\\infty}$ functions $C^{\\infty}$ maps Tangent spaces Differentials of $C^{\\infty}$ maps Examples of differentials of $C^{\\infty}$ maps; local properties of maps ","date":"16 octubre 2023","externalUrl":null,"permalink":"/lecture/2023w_geometryiia/","section":"Teaching","summary":"Term 3, Mon. Period 3 · Faculty of Science, Niigata University","title":"Geometry IIA","type":"lecture"},{"content":"Semester 2, Mon. Period 4 (co-taught) · Graduate School of Science and Technology, Niigata University\nSyllabus\nCourse contents\nDifferential geometry of curves and road design (11/1) Topology and protein structures (11/6) ","date":"16 octubre 2023","externalUrl":null,"permalink":"/lecture/2023s_shizenkagakusouron1/","section":"Teaching","summary":"Semester 2, Mon. Period 4 (co-taught) · Graduate School of Science and Technology, Niigata University","title":"Overview of Natural Sciences I","type":"lecture"},{"content":"For doctoral students; Semester 2, Thu. Period 3 · Graduate School of Science and Technology, Niigata University\nSyllabus\nTextbooks\nJohn W. Milnor, \u0026ldquo;Morse Theory\u0026rdquo;, Princeton University Press Course contents\nReview of Morse theory on finite-dimensional manifolds Review of Riemannian geometry Review of Morse theory on path spaces Applications to Lie groups and symmetric spaces ","date":"5 octubre 2023","externalUrl":null,"permalink":"/lecture/2023w_difftopod/","section":"Teaching","summary":"For doctoral students; Semester 2, Thu. Period 3 · Graduate School of Science and Technology, Niigata University","title":"Differential Topology","type":"lecture"},{"content":"Term 2, Fri. Period 4 (co-taught) · Faculty of Science, Niigata University\nSyllabus\nTextbooks\nY. Takahashi and M. Kato, \u0026ldquo;微分積分概論 [新訂版]\u0026rdquo; (in Japanese), Saiensu-sha T. Tanaka, H. Kojima, A. Hoshi, R. Orita, N. Innami, and H. Yoshihara, \u0026ldquo;要点明解 線形代数 三訂版\u0026rdquo; (in Japanese), Baifukan ","date":"9 junio 2023","externalUrl":null,"permalink":"/lecture/2023s_kisoenshu_b/","section":"Teaching","summary":"Term 2, Fri. Period 4 (co-taught) · Faculty of Science, Niigata University","title":"Basic Exercises in Mathematics b","type":"lecture"},{"content":"Term 2, Thu. Periods 1–2 (co-taught) · Faculty of Science, Niigata University\nSyllabus\nTextbooks\nF. Sato, \u0026ldquo;数学ビギナーズマニュアル [第2版]\u0026rdquo; (in Japanese), Nippon Hyoron Sha ","date":"8 junio 2023","externalUrl":null,"permalink":"/lecture/2023s_rigakukisoenshu/","section":"Teaching","summary":"Term 2, Thu. Periods 1–2 (co-taught) · Faculty of Science, Niigata University","title":"Basic Seminar in Science (Mathematics Program)","type":"lecture"},{"content":"Term 2, Mon. Period 3 \u0026amp; Thu. Period 4 · Faculty of Science, Niigata University\nSyllabus\nNote\nHeld on Mon. Period 3 \u0026amp; Thu. Period 4.\nTextbooks\nK. Komiya, \u0026ldquo;位相幾何入門\u0026rdquo; (in Japanese), Shokabo Main references\nI. Tamura, \u0026ldquo;トポロジー\u0026rdquo; (in Japanese), Iwanami Zensho Recommended reading\nY. Hiraoka, \u0026ldquo;タンパク質構造とトポロジー\u0026rdquo; (in Japanese), Kyoritsu Shuppan Course contents\nTopological spaces Quotient spaces; closed surfaces and connected sums Classification of closed surfaces Simplices and simplicial complexes Skeletons and polyhedra; group theory, part 1 Group theory, part 2; oriented simplices Chain groups and homology groups Midterm exam Computing homology groups; simplicial maps Chain homomorphisms; homology groups of polyhedra, part 1 (definitions); homotopy Homology groups of polyhedra, part 2 (homotopy invariance) Euler numbers; homology groups and homomorphisms The Mayer-Vietoris exact sequence Homology groups of closed surfaces Persistent homology groups and protein structures End-of-term exam and summary ","date":"8 junio 2023","externalUrl":null,"permalink":"/lecture/2023s_geometryib/","section":"Teaching","summary":"Term 2, Mon. Period 3 \u0026 Thu. Period 4 · Faculty of Science, Niigata University","title":"Geometry IB","type":"lecture"},{"content":"Term 1, Fri. Period 4 (co-taught) · Faculty of Science, Niigata University\nSyllabus\nTextbooks\nY. Takahashi and M. Kato, \u0026ldquo;微分積分概論 [新訂版]\u0026rdquo; (in Japanese), Saiensu-sha T. Tanaka, H. Kojima, A. Hoshi, R. Orita, N. Innami, and H. Yoshihara, \u0026ldquo;要点明解 線形代数 三訂版\u0026rdquo; (in Japanese), Baifukan ","date":"7 abril 2023","externalUrl":null,"permalink":"/lecture/2023s_kisoenshu_a/","section":"Teaching","summary":"Term 1, Fri. Period 4 (co-taught) · Faculty of Science, Niigata University","title":"Basic Exercises in Mathematics a","type":"lecture"},{"content":"Term 1, Mon. Period 3 \u0026amp; Thu. Period 2 · Faculty of Science, Niigata University\nSyllabus\nTextbooks\nM. Umehara and K. Yamada, \u0026ldquo;曲線と曲面（改訂版）\u0026rdquo; (in Japanese), Shokabo Main references\nS. Kobayashi, \u0026ldquo;曲線と曲面の微分幾何（改訂版）\u0026rdquo; (in Japanese), Shokabo Recommended reading\nManfredo P. do Carmo, Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition, Dover Publications Course contents\nWhat is a curve? Curvature The Frenet formulas The fundamental theorem of plane curves; the four-vertex theorem Space curves Midterm exam What is a surface? The first fundamental form, part 1 (definition) The first fundamental form, part 2 (areas and lengths) The first fundamental form, part 3 (angles, maps); the second fundamental form, part 1 (definition) The second fundamental form, part 2 (curvatures, invariance) The second fundamental form, part 3 (the Weingarten formulas); definition of normal curvature Normal and principal curvatures; geodesics Theorema Egregium; the Gauss-Bonnet theorem End-of-term exam and summary ","date":"6 abril 2023","externalUrl":null,"permalink":"/lecture/2023s_geometryia/","section":"Teaching","summary":"Term 1, Mon. Period 3 \u0026 Thu. Period 2 · Faculty of Science, Niigata University","title":"Geometry IA","type":"lecture"},{"content":"For master\u0026rsquo;s students; Semester 1, Thu. Period 3 · Graduate School of Science and Technology, Niigata University\nSyllabus\nTextbooks\nJ. W. Milnor and J. D. Stashef \u0026ldquo;Characteristic Classes\u0026rdquo; Annals of Mathematics Studies Course contents\nDifferentiable manifolds Vector bundles, part 1 (definitions, examples) Vector bundles, part 2 (the canonical line bundle, sections) Vector bundles, part 3 (Euclidean vector bundles, induced bundles) Vector bundles, part 4 (Whitney sums, orthogonal complement bundles) Singular homology and cohomology (basic definitions, cup products) Stiefel-Whitney classes, part 1 Stiefel-Whitney classes, part 2 Stiefel-Whitney classes, part 3 Stiefel-Whitney classes, part 4; Grassmann manifolds, part 1 Grassmann manifolds, part 2 Grassmann manifolds, part 3; universal bundles Classifying maps; characteristic classes H*(Gr;Z/2Z); Pontryagin, Euler, and Chern classes ","date":"6 abril 2023","externalUrl":null,"permalink":"/lecture/2023s_difftopom/","section":"Teaching","summary":"For master’s students; Semester 1, Thu. Period 3 · Graduate School of Science and Technology, Niigata University","title":"Topics in Differential Topology","type":"lecture"},{"content":"M2: 3, M1: 1, B4: 6 (AY 2023) · Faculty of Science and Graduate School of Science and Technology, Niigata University\nMembers (AY 2023) # Orita 9/19 9/22a 9/22b 10/12a 10/12b 10/19 10/20 10/26 11/2 M2 # KK: Multiparameter persistence modules 4/18 5/16 5/16 7/4 8/1 8/9 8/24 8/29 9/4 9/13 9/19 10/10 10/17 10/24 10/31 11/14 11/21 11/30 12/5 12/12 12/26 KY: Algebraic topology and Morse theory 4/11 5/9 5/23 6/27a 6/27b 7/11 7/18 7/25 8/1 8/9 8/24 8/29 9/4 9/13 9/19 9/26a 9/26b 10/3 10/17 10/24 10/31 11/7 11/14a 11/14b 11/30 12/5 12/12 12/19 12/26 2/20 3/5 3/12 3/19 YY: Function theory on symplectic manifolds 5/9 5/30a 5/30b 7/4 7/18 8/1 8/9 8/24 9/13 10/3 10/10 10/17 10/31 11/7 11/21 11/30 12/12 12/19 12/26 M1 # KY: Riemann surfaces 4/11 4/18 5/16 5/23 6/13 7/11 7/25 10/10 10/24 11/7 11/21 12/19 1/25 2/6 2/13 2/22 B4 # KO (graduated on September 20, 2023) RS, SY: \u0026ldquo;Algebraic Topology\u0026rdquo; by Allen Hatcher 4/10a 4/10b 4/24 5/8 5/22 5/29 6/12 6/19 6/26 7/3 7/20 7/24 10/16 10/23 10/30 11/6 11/20 12/4 12/11 12/25 1/16 1/30 YS, TH: \u0026ldquo;Morse理論の基礎\u0026rdquo; by Y. Matsumoto (in Japanese) 4/17a 4/17b 5/15a 5/15b 5/29 6/5 6/12 6/19 7/3 7/10 7/20 7/24 10/30 11/1 11/13 11/20 12/11 12/18 12/25 1/22 1/30 SE: \u0026ldquo;結び目の理論\u0026rdquo; by A. Kawauchi (in Japanese) 4/24 5/22 6/5 6/26 7/10 10/16 10/23 12/4 1/22 \u0026ldquo;Mathematical Methods of Classical Mechanics\u0026rdquo; by Vladimir I. Arnold 2/14 2/21 3/7 3/14 4/18 5/9 5/16 ","date":"1 abril 2023","externalUrl":null,"permalink":"/lecture/2023_zemi/","section":"Teaching","summary":"M2: 3, M1: 1, B4: 6 (AY 2023) · Faculty of Science and Graduate School of Science and Technology, Niigata University","title":"Research Group (Seminar)","type":"lecture"},{"content":"Term 4, Mon. Period 3 · Faculty of Science, Niigata University\nSyllabus\nTextbooks\nY. Matsumoto, \u0026ldquo;多様体の基礎\u0026rdquo; (in Japanese), University of Tokyo Press Main references\nL. W. Tu, \u0026ldquo;An Introduction to Manifolds\u0026rdquo; (Japanese translation by M. Masuda, H. Abe, and T. Horiguchi, Shokabo) Y. Matsushima, \u0026ldquo;多様体入門\u0026rdquo; (in Japanese), Shokabo Recommended reading\nR. Bott and L. W. Tu, \u0026ldquo;Differential Forms in Algebraic Topology\u0026rdquo; (Japanese translation by M. Mimura, Maruzen) Course contents\nImmersions and embeddings The embedding theorem; partitions of unity Regular and critical points Vector fields, part 1 Vector fields, part 2 Differential forms, part 1 Differential forms, part 2 Differential forms, part 3 ","date":"5 diciembre 2022","externalUrl":null,"permalink":"/lecture/2022w_geometryiib/","section":"Teaching","summary":"Term 4, Mon. Period 3 · Faculty of Science, Niigata University","title":"Geometry IIB","type":"lecture"},{"content":"For doctoral students; Semester 2, Thu. Period 3 · Graduate School of Science and Technology, Niigata University\nSyllabus\nTextbooks\nJohn W. Milnor, \u0026ldquo;Morse Theory\u0026rdquo;, Princeton University Press Course contents\nReview of Morse theory on finite-dimensional manifolds Review of Riemannian geometry Review of Morse theory on path spaces Applications to Lie groups and symmetric spaces ","date":"6 octubre 2022","externalUrl":null,"permalink":"/lecture/2022w_difftopod/","section":"Teaching","summary":"For doctoral students; Semester 2, Thu. Period 3 · Graduate School of Science and Technology, Niigata University","title":"Differential Topology","type":"lecture"},{"content":"Term 3, Wed. Periods 4–5 (co-taught) · Niigata University\nSyllabus\nNote\nThis class is held online via Zoom.\nCourse contents (Orita\u0026rsquo;s part)\nEuler numbers and polyhedra — Euler\u0026rsquo;s polyhedron formula Euler numbers and wind flows — the Poincaré–Hopf theorem Euler numbers and critical points of functions — Morse\u0026rsquo;s theorem Euler numbers and the curvature of surfaces — the Gauss–Bonnet theorem ","date":"5 octubre 2022","externalUrl":null,"permalink":"/lecture/2022w_the_world/","section":"Teaching","summary":"Term 3, Wed. Periods 4–5 (co-taught) · Niigata University","title":"The World of Mathematics","type":"lecture"},{"content":"Term 3, Mon. Period 3 · Faculty of Science, Niigata University\nSyllabus\nTextbooks\nY. Matsumoto, \u0026ldquo;多様体の基礎\u0026rdquo; (in Japanese), University of Tokyo Press Main references\nL. W. Tu, \u0026ldquo;An Introduction to Manifolds\u0026rdquo; (Japanese translation by M. Masuda, H. Abe, and T. Horiguchi, Shokabo) Y. Matsushima, \u0026ldquo;多様体入門\u0026rdquo; (in Japanese), Shokabo Course contents\nDefinition of manifolds Examples of manifolds $C^{\\infty}$ functions $C^{\\infty}$ maps; directional derivatives Tangent spaces Differentials of $C^{\\infty}$ maps Examples of differentials of $C^{\\infty}$ maps; local properties of maps, part 1 Local properties of maps, part 2; projective spaces ","date":"3 octubre 2022","externalUrl":null,"permalink":"/lecture/2022w_geometryiia/","section":"Teaching","summary":"Term 3, Mon. Period 3 · Faculty of Science, Niigata University","title":"Geometry IIA","type":"lecture"},{"content":"Semester 1 intensive course by Prof. Tatsuya Miura (Tokyo Institute of Technology) · Graduate School of Science and Technology, Niigata University\nSyllabus\nCourse contents\nSessions 1–2: introduction to the elastic curve model Sessions 3–5: classification of classical elastic curves Sessions 6–8: variational analysis of elastic curves and further topics ","date":"24 agosto 2022","externalUrl":null,"permalink":"/lecture/2022s_sentansouron/","section":"Teaching","summary":"Semester 1 intensive course by Prof. Tatsuya Miura (Tokyo Institute of Technology) · Graduate School of Science and Technology, Niigata University","title":"Overview of Advanced Science and Technology","type":"lecture"},{"content":"Morimichi Kawasaki, Ryuma Orita\nJournal of the Mathematical Society of Japan, vol. 74 (2022), no. 3, pp. 829–847\n· Abstract # (Non-)displaceability of fibers of integrable systems has been an important problem in symplectic geometry. In this paper, for a large class of classical Liouville integrable systems containing the Lagrangian top, the Kovalevskaya top and the C. Neumann problem, we find a non-displaceable fiber for each of them. Moreover, we show that the non-displaceable fiber which we detect is the unique fiber which is non-displaceable from the zero-section. As a special case of this result, we also show the existence of a singular level set of a convex Hamiltonian, which is non-displaceable from the zero-section. To prove these results, we use the notion of superheaviness introduced by Entov and Polterovich.\n","date":"1 julio 2022","externalUrl":null,"permalink":"/publication/08-rigid-fibers/","section":"Publications","summary":"Morimichi Kawasaki, Ryuma Orita — Journal of the Mathematical Society of Japan, vol. 74 (2022), no. 3, pp. 829–847","title":"Rigid fibers of integrable systems on cotangent bundles","type":"publication"},{"content":"Term 2, Fri. Period 4 (co-taught) · Faculty of Science, Niigata University\nSyllabus\nNote\nThis class is held online via Zoom.\nTextbooks\nY. Takahashi and M. Kato, \u0026ldquo;微分積分概論 [新訂版]\u0026rdquo; (in Japanese), Saiensu-sha T. Tanaka, H. Kojima, A. Hoshi, R. Orita, N. Innami, and H. Yoshihara, \u0026ldquo;要点明解 線形代数 三訂版\u0026rdquo; (in Japanese), Baifukan ","date":"17 junio 2022","externalUrl":null,"permalink":"/lecture/2022s_kisoenshu_b/","section":"Teaching","summary":"Term 2, Fri. Period 4 (co-taught) · Faculty of Science, Niigata University","title":"Basic Exercises in Mathematics b","type":"lecture"},{"content":"Term 2, Thu. Periods 1–2 (co-taught) · Faculty of Science, Niigata University\nSyllabus\nTextbooks\nF. Sato, \u0026ldquo;数学ビギナーズマニュアル [第2版]\u0026rdquo; (in Japanese), Nippon Hyoron Sha ","date":"16 junio 2022","externalUrl":null,"permalink":"/lecture/2022s_rigakukisoenshu/","section":"Teaching","summary":"Term 2, Thu. Periods 1–2 (co-taught) · Faculty of Science, Niigata University","title":"Basic Seminar in Science (Mathematics Program)","type":"lecture"},{"content":"Term 2, Mon. Period 3 \u0026amp; Thu. Period 4 · Faculty of Science, Niigata University\nSyllabus\nNote\nHeld on Mon. Period 3 \u0026amp; Thu. Period 4.\nMain references\nM. Umehara and K. Yamada, \u0026ldquo;曲線と曲面（改訂版）\u0026rdquo; (in Japanese), Shokabo Recommended reading\nS. Kobayashi, \u0026ldquo;曲線と曲面の微分幾何（改訂版）\u0026rdquo; (in Japanese), Shokabo Manfredo P. do Carmo, Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition, Dover Publications Course contents\nWhat is a surface? Exercises The first fundamental form, part 1 (definition) Exercises The first fundamental form, part 2 (areas, lengths, and angles) Exercises The second fundamental form, part 1 (definition, curvatures) Exercises The second fundamental form, part 2 (examples, invariance) Exercises Normal curvature; principal directions Exercises Umbilical points; asymptotic directions; geodesics Exercises Theorema Egregium; the Gauss–Bonnet theorem End-of-term exam and summary ","date":"13 junio 2022","externalUrl":null,"permalink":"/lecture/2022s_geometryib/","section":"Teaching","summary":"Term 2, Mon. Period 3 \u0026 Thu. Period 4 · Faculty of Science, Niigata University","title":"Geometry IB","type":"lecture"},{"content":"Term 1, Fri. Period 4 (co-taught) · Faculty of Science, Niigata University\nSyllabus\nNote\nThis class is held online via Zoom.\nTextbooks\nY. Takahashi and M. Kato, \u0026ldquo;微分積分概論 [新訂版]\u0026rdquo; (in Japanese), Saiensu-sha T. Tanaka, H. Kojima, A. Hoshi, R. Orita, N. Innami, and H. Yoshihara, \u0026ldquo;要点明解 線形代数 三訂版\u0026rdquo; (in Japanese), Baifukan ","date":"8 abril 2022","externalUrl":null,"permalink":"/lecture/2022s_kisoenshu_a/","section":"Teaching","summary":"Term 1, Fri. Period 4 (co-taught) · Faculty of Science, Niigata University","title":"Basic Exercises in Mathematics a","type":"lecture"},{"content":"Tamaki Tanaka, Hideo Kojima, Akinari Hoshi, Ryuma Orita, Nobuhiro Innami, Hisao Yoshihara\nBaifukan\nAbstract # This textbook for beginners summarizes the basic content of linear algebra that students specializing in the field of natural science should know. The book is designed to meet the needs of those who use linear algebra in the field, namely, to first learn mathematics \u0026lsquo;\u0026lsquo;as a tool,\u0026rsquo;\u0026rsquo; \u0026lsquo;\u0026lsquo;as a language for describing phenomena,\u0026rsquo;\u0026rsquo; and \u0026lsquo;\u0026lsquo;for immediate use,\u0026rsquo;\u0026rsquo; omitting proofs and the like as much as possible and not being too concerned with logical rigor, while keeping the main points of linear algebra easy to understand. The book is explained in the following manner. In the third edition, a new chapter has been added to explain what vectors are. (Translated with www.DeepL.com/Translator (free version))\n","date":"8 abril 2022","externalUrl":null,"permalink":"/publication/09-linear-math/","section":"Publications","summary":"Tamaki Tanaka, Hideo Kojima, Akinari Hoshi, Ryuma Orita, Nobuhiro Innami, Hisao Yoshihara — Baifukan","title":"Linear Mathematics, Third Edition (Japanese)","type":"publication"},{"content":"Term 1, Mon. Period 3 \u0026amp; Thu. Period 2 · Faculty of Science, Niigata University\nSyllabus\nMain references\nManfredo P. do Carmo, Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition, Dover Publications Recommended reading\nS. Kobayashi, \u0026ldquo;曲線と曲面の微分幾何（改訂版）\u0026rdquo; (in Japanese), Shokabo M. Umehara and K. Yamada, \u0026ldquo;曲線と曲面（改訂版）\u0026rdquo; (in Japanese), Shokabo Course contents\nParametrized differentiable curves Exercises Regular curves; arc length Exercises Curvature of curves Exercises Torsion of curves; the Frenet–Serret formulas Exercises The fundamental theorem of space curves Exercises The Jordan curve theorem; the rotation index theorem Exercises The four-vertex theorem Exercises The isoperimetric problem; the inscribed rectangle problem End-of-term exam and summary ","date":"7 abril 2022","externalUrl":null,"permalink":"/lecture/2022s_geometryia/","section":"Teaching","summary":"Term 1, Mon. Period 3 \u0026 Thu. Period 2 · Faculty of Science, Niigata University","title":"Geometry IA","type":"lecture"},{"content":"For master\u0026rsquo;s students; Semester 1, Thu. Period 3 · Graduate School of Science and Technology, Niigata University\nSyllabus\nTextbooks\nAna Cannas da Silva, \u0026ldquo;Lectures on Symplectic Geometry\u0026rdquo;, Springer Course contents\nSymplectic vector spaces Symplectic manifolds; cotangent bundles The tautological 1-form and the canonical 2-form Lagrangian submanifolds of cotangent bundles Conormal bundles; constructing symplectomorphisms The method of generating functions; applications to geodesic flow Periodic points; billiards; recurrence Isotopies and time-dependent vector fields; Lie derivatives Interior products; Cartan\u0026rsquo;s formula; Hamiltonian diffeomorphisms The Moser trick Moser stability; Moser isotopies; Darboux\u0026rsquo;s theorem Weinstein\u0026rsquo;s Lagrangian neighborhood theorem Weinstein\u0026rsquo;s tubular neighborhood theorem; the tangent space of the symplectomorphism group The Arnol\u0026rsquo;d conjecture; non-displaceability; partial symplectic quasi-states Heavy and superheavy sets Motion of a spinning top and superheavy sets ","date":"7 abril 2022","externalUrl":null,"permalink":"/lecture/2022s_difftopom/","section":"Teaching","summary":"For master’s students; Semester 1, Thu. Period 3 · Graduate School of Science and Technology, Niigata University","title":"Topics in Differential Topology","type":"lecture"},{"content":"M1: 3, B4: 4 (AY 2022) · Faculty of Science and Graduate School of Science and Technology, Niigata University\nMembers (AY 2022) # Orita 6/6a 6/6b 6/14 12/19a 12/19b 12/19c 12/19c M1 # KK 4/12 4/26 5/17 5/31 6/21 6/28 7/12 8/2 8/29a 8/29b 9/29 10/11 10/25a 10/25b 11/8 11/22 12/6 1/10 1/24 2/7 KY 4/12H 4/19M 4/26H 5/10M 5/17H 5/24M 5/31H 6/7M 6/14M 6/21H 6/28H 7/5M 7/12H 7/19H 8/2M 8/18H 8/23M 8/30H 9/12M 9/20H 10/4M 10/11H 10/18M 10/25H 11/1 11/8 11/15 11/22 11/29 12/6 12/15 1/10 1/17 1/24 2/7 2/14 2/21 3/7 3/14 3/30 YY 4/19 5/10 5/24 6/7 6/14 7/5 7/19 9/5a 9/5b 9/12 9/27 10/4 10/18 11/1 11/15 11/29a 11/29b 12/15 1/17 1/31 B4 # KO RC: \u0026ldquo;Algebraic Topology\u0026rdquo; by Allen Hatcher 4/11 4/18 5/2 5/9 5/23 5/30 6/13 7/11 8/1 10/17 10/24 11/7 11/14 11/28 12/5 12/26 1/23 2/6 2/13 YN, KY: \u0026ldquo;An Introduction to Manifolds\u0026rdquo; by Loring W. Tu 4/11 4/18 4/25a 4/25b 5/2 5/9 5/16a 5/16b 6/13 6/20a 6/20b 6/27a 6/27b 7/4a 7/4b 7/11 8/1 10/3a 10/3b 10/17 10/24 10/31a 10/31b 11/7 11/14 11/21a 11/21b 11/28 12/5 12/12a 12/12b 12/26 1/23 1/30a 1/30b 2/6 2/13 ","date":"1 abril 2022","externalUrl":null,"permalink":"/lecture/2022_zemi/","section":"Teaching","summary":"M1: 3, B4: 4 (AY 2022) · Faculty of Science and Graduate School of Science and Technology, Niigata University","title":"Research Group (Seminar)","type":"lecture"},{"content":"Seminar\nKIAS (Zoom)\n","date":"4 febrero 2022","externalUrl":null,"permalink":"/talk/2022-02-kias/","section":"Talks","summary":"Seminar · KIAS (Zoom)","title":"A hierarchy of rigid subsets of symplectic manifolds","type":"talk"},{"content":"AS-NCTS Seminar on Geometry\nAcademia Sinica \u0026amp; NCTS, National Taiwan University (Webex)\n","date":"24 diciembre 2021","externalUrl":null,"permalink":"/talk/2021-12-ncts/","section":"Talks","summary":"AS-NCTS Seminar on Geometry · Academia Sinica \u0026 NCTS, National Taiwan University (Webex)","title":"A hierarchy of rigid subsets of symplectic manifolds","type":"talk"},{"content":"Term 4, Mon. Period 3 · Faculty of Science, Niigata University\nSyllabus\nNote\nThis course is held online via Zoom.\nTextbooks\nY. Matsumoto, \u0026ldquo;多様体の基礎\u0026rdquo; (in Japanese), University of Tokyo Press Main references\nL. W. Tu, \u0026ldquo;An Introduction to Manifolds\u0026rdquo; (Japanese translation by M. Masuda, H. Abe, and T. Horiguchi, Shokabo) Recommended reading\nR. Bott and L. W. Tu, \u0026ldquo;Differential Forms in Algebraic Topology\u0026rdquo; (Japanese translation by M. Mimura, Maruzen) Course contents\nProjective spaces Immersions and embeddings The embedding theorem; partitions of unity Regular and critical points Vector fields, part 1 Vector fields, part 2 Differential forms, part 1 Differential forms, part 2 ","date":"6 diciembre 2021","externalUrl":null,"permalink":"/lecture/2021w_geometryiib/","section":"Teaching","summary":"Term 4, Mon. Period 3 · Faculty of Science, Niigata University","title":"Geometry IIB","type":"lecture"},{"content":"The 3rd Japan-Taiwan Joint Conference on Differential Geometry\nOCAMI, Osaka City University \u0026amp; NCTS, National Taiwan University (Webex)\n","date":"2 noviembre 2021","externalUrl":null,"permalink":"/talk/2021-11-ocu/","section":"Talks","summary":"The 3rd Japan-Taiwan Joint Conference on Differential Geometry · OCAMI, Osaka City University \u0026 NCTS, National Taiwan University (Webex)","title":"Rigid fibers of integrable systems on cotangent bundles","type":"talk"},{"content":"For doctoral students; Semester 2, Thu. Period 3 · Graduate School of Science and Technology, Niigata University\nSyllabus\nNote\nThis course is held online via Zoom.\nTextbooks\nJohn W. Milnor, \u0026ldquo;Morse Theory\u0026rdquo;, Princeton University Press\nCourse contents\nCovariant differentiation, part 1 Covariant differentiation, part 2 The curvature tensor Geodesics and completeness, part 1 Geodesics and completeness, part 2 Geodesics and completeness, part 3 The path space of a smooth manifold The energy of a path The Hessian of the energy function at critical paths Jacobi fields: the null space of $\\mathrm{Hess}_{\\gamma}(E)$, part 1 Jacobi fields: the null space of $\\mathrm{Hess}_{\\gamma}(E)$, part 2; the index theorem, part 1 The index theorem, part 2 A finite-dimensional approximation to $\\Omega^c$, part 1 A finite-dimensional approximation to $\\Omega^c$, part 2; the topology of the full path space, part 1 The topology of the full path space, part 2 Existence of non-conjugate points Some relations between topology and curvature, part 1 Some relations between topology and curvature, part 2 ","date":"7 octubre 2021","externalUrl":null,"permalink":"/lecture/2021w_difftopod/","section":"Teaching","summary":"For doctoral students; Semester 2, Thu. Period 3 · Graduate School of Science and Technology, Niigata University","title":"Differential Topology","type":"lecture"},{"content":"Term 3, Wed. Periods 4–5 (co-taught) · Niigata University\nSyllabus\nNote\nThis course is held online via Zoom.\nCourse contents (Orita\u0026rsquo;s part)\nEuler numbers and polyhedra — Euler\u0026rsquo;s polyhedron formula Euler numbers and wind flows — the Poincaré–Hopf theorem Euler numbers and critical points of functions — Morse\u0026rsquo;s theorem Euler numbers and the curvature of surfaces — the Gauss–Bonnet theorem ","date":"6 octubre 2021","externalUrl":null,"permalink":"/lecture/2021w_the_world/","section":"Teaching","summary":"Term 3, Wed. Periods 4–5 (co-taught) · Niigata University","title":"The World of Mathematics","type":"lecture"},{"content":"Term 3, Mon. Period 3 · Faculty of Science, Niigata University\nSyllabus\nNote\nThis course is held online via Zoom.\nTextbooks\nY. Matsumoto, \u0026ldquo;多様体の基礎\u0026rdquo; (in Japanese), University of Tokyo Press Main references\nL. W. Tu, \u0026ldquo;An Introduction to Manifolds\u0026rdquo; (Japanese translation by M. Masuda, H. Abe, and T. Horiguchi, Shokabo) Course contents\nDefinition of manifolds Examples of manifolds $C^s$ functions and $C^s$ maps $C^s$ diffeomorphisms; directional derivatives Tangent spaces Differentials of $C^r$ maps, part 1 Differentials of $C^r$ maps, part 2 Local properties of maps ","date":"4 octubre 2021","externalUrl":null,"permalink":"/lecture/2021w_geometryiia/","section":"Teaching","summary":"Term 3, Mon. Period 3 · Faculty of Science, Niigata University","title":"Geometry IIA","type":"lecture"},{"content":"For master\u0026rsquo;s students; Semester 1, intensive course · Graduate School of Science and Technology, Niigata University\nSyllabus\nNote\nThis course is held online via Zoom.\nTextbooks\nY. Hiraoka, \u0026ldquo;タンパク質構造とトポロジー\u0026rdquo; (in Japanese), Kyoritsu Shuppan Course contents\nSimplicial complexes; abstract simplicial complexes; homotopy The nerve theorem, part 1 The nerve theorem, part 2; simplicial-complex models of proteins Groups and rings Modules over rings Homology groups, part 1 Homology groups, part 2 Homology groups of proteins; $\\mathbb{Z}/2\\mathbb{Z}\\lbrack x \\rbrack$-modules Persistent homology groups, part 1 Persistent homology groups, part 2; persistent homology groups of proteins ","date":"13 septiembre 2021","externalUrl":null,"permalink":"/lecture/2021s_difftopom/","section":"Teaching","summary":"For master’s students; Semester 1, intensive course · Graduate School of Science and Technology, Niigata University","title":"Topics in Differential Topology","type":"lecture"},{"content":"Term 2, Fri. Period 4 (co-taught) · Faculty of Science, Niigata University\nSyllabus\nNote\nThese exercise sessions are held online via Zoom.\nTextbooks\nY. Takahashi and M. Kato, \u0026ldquo;微分積分概論 [新訂版]\u0026rdquo; (in Japanese), Saiensu-sha N. Innami, T. Tanaka, H. Kojima, and A. Hoshi, \u0026ldquo;要点明解 線形代数\u0026rdquo; (in Japanese), Baifukan ","date":"11 junio 2021","externalUrl":null,"permalink":"/lecture/2021s_kisoenshu_b/","section":"Teaching","summary":"Term 2, Fri. Period 4 (co-taught) · Faculty of Science, Niigata University","title":"Basic Exercises in Mathematics b","type":"lecture"},{"content":"Term 2, Mon. Period 3 \u0026amp; Thu. Period 2 · Faculty of Science, Niigata University\nSyllabus\nNote\nThis course is held online via Zoom.\nMain references\nManfredo P. do Carmo, Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition, Dover Publications Recommended reading\nS. Kobayashi, \u0026ldquo;曲線と曲面の微分幾何（改訂版）\u0026rdquo; (in Japanese), Shokabo M. Umehara and K. Yamada, \u0026ldquo;曲線と曲面（改訂版）\u0026rdquo; (in Japanese), Shokabo Course contents\nSpheres The implicit function theorem and the inverse function theorem Definition of regular surfaces Examples of regular surfaces The implicit function theorem and regular surfaces, part 1 The implicit function theorem and regular surfaces, part 2; $C^{\\infty}$ functions on surfaces, part 1 $C^{\\infty}$ functions on surfaces, part 2; $C^{\\infty}$ maps between surfaces, part 1 $C^{\\infty}$ maps between surfaces, part 2; tangent planes Differentials The first fundamental form, part 1 (definition, examples, lengths of curves on surfaces) The first fundamental form, part 2 (loxodromes, areas of regions on surfaces) The Gauss map Self-adjoint maps and quadratic forms; the second fundamental form The second fundamental form; the various curvatures Gauss\u0026rsquo;s Theorema Egregium and the Gauss–Bonnet theorem End-of-term exam and summary ","date":"10 junio 2021","externalUrl":null,"permalink":"/lecture/2021s_geometryib/","section":"Teaching","summary":"Term 2, Mon. Period 3 \u0026 Thu. Period 2 · Faculty of Science, Niigata University","title":"Geometry IB","type":"lecture"},{"content":"Term 1, Fri. Period 4 (co-taught) · Faculty of Science, Niigata University\nSyllabus\nNote\nThese exercise sessions are held online via Zoom.\nTextbooks\nY. Takahashi and M. Kato, \u0026ldquo;微分積分概論 [新訂版]\u0026rdquo; (in Japanese), Saiensu-sha N. Innami, T. Tanaka, H. Kojima, and A. Hoshi, \u0026ldquo;要点明解 線形代数\u0026rdquo; (in Japanese), Baifukan ","date":"9 abril 2021","externalUrl":null,"permalink":"/lecture/2021s_kisoenshu_a/","section":"Teaching","summary":"Term 1, Fri. Period 4 (co-taught) · Faculty of Science, Niigata University","title":"Basic Exercises in Mathematics a","type":"lecture"},{"content":"Term 1, Mon. Period 3 \u0026amp; Thu. Period 2 · Faculty of Science, Niigata University\nSyllabus\nNote\nThis course is held online via Zoom.\nMain references\nManfredo P. do Carmo, Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition, Dover Publications Recommended reading\nS. Kobayashi, \u0026ldquo;曲線と曲面の微分幾何（改訂版）\u0026rdquo; (in Japanese), Shokabo M. Umehara and K. Yamada, \u0026ldquo;曲線と曲面（改訂版）\u0026rdquo; (in Japanese), Shokabo Course contents\nParametrized differentiable curves; inner products Exercises Regular curves; arc length; orientation of vector spaces Exercises Cross products; curvature of curves; principal normal vectors Exercises Binormal vectors; torsion Exercises The Frenet–Serret formulas; the fundamental theorem of space curves Exercises Local canonical form; closed curves Exercises The Jordan curve theorem; the rotation index theorem; the four-vertex theorem Exercises Proof of the four-vertex theorem; the isoperimetric inequality End-of-term exam and summary ","date":"8 abril 2021","externalUrl":null,"permalink":"/lecture/2021s_geometryia/","section":"Teaching","summary":"Term 1, Mon. Period 3 \u0026 Thu. Period 2 · Faculty of Science, Niigata University","title":"Geometry IA","type":"lecture"},{"content":"B4: 4 (AY 2021) · Faculty of Science, Niigata University\nMembers (AY 2021) # B4 # KO, YY: \u0026ldquo;多様体の基礎\u0026rdquo; by Y. Matsumoto (in Japanese) 4/14 4/21 4/28 5/7 5/12 5/19 5/26 6/2 6/9 6/16 6/23 6/30 7/7 7/14 7/21 7/28 10/6 10/13 10/20 10/27 11/10 11/17 11/24 12/8 12/15 12/22 1/19 1/26 2/2 2/9 KK: \u0026ldquo;代数的トポロジー\u0026rdquo; by M. Masuda (in Japanese) 4/14 4/28 6/2 6/16 6/30 7/14 7/27 10/6 10/20 10/27 11/10 11/24 12/8 12/22 1/19 2/2 KY: \u0026ldquo;Algebraic Topology\u0026rdquo; by Allen Hatcher 4/21 5/7 5/26 6/9 6/23 7/7 7/20 8/4 10/13 11/1 11/17 12/3 12/15 1/12 1/26 2/9 2/17 2/24 3/3 3/10 3/24 3/31 ","date":"1 abril 2021","externalUrl":null,"permalink":"/lecture/2021_zemi/","section":"Teaching","summary":"B4: 4 (AY 2021) · Faculty of Science, Niigata University","title":"Research Group (Seminar)","type":"lecture"},{"content":"Term 4, Mon. Period 3 · Faculty of Science, Niigata University\nNote\nThis course is held online via Zoom.\nReferences\nManfredo P. do Carmo, Differential Geometry of Curves and Surfaces, Dover Publications\nCourse contents\n$C^{\\infty}$ functions on surfaces $C^{\\infty}$ maps between surfaces Tangent planes and differentials The first fundamental form, part 1 (definition, examples, lengths of curves on surfaces) The first fundamental form, part 2 (loxodromes, areas of regions on surfaces) The Gauss map; the second fundamental form Gaussian curvature; the Gauss–Bonnet theorem End-of-term exam ","date":"7 diciembre 2020","externalUrl":null,"permalink":"/lecture/2020w_geometryiib/","section":"Teaching","summary":"Term 4, Mon. Period 3 · Faculty of Science, Niigata University","title":"Geometry IIB","type":"lecture"},{"content":"12th International Symposium on Natural Sciences\nIncheon National University, South Korea (Zoom)\n","date":"7 octubre 2020","externalUrl":null,"permalink":"/talk/2020-10-incheon/","section":"Talks","summary":"12th International Symposium on Natural Sciences · Incheon National University, South Korea (Zoom)","title":"Pseudoheavy subsets in symplectic manifolds","type":"talk"},{"content":"Term 3, Mon. Period 3 · Faculty of Science, Niigata University\nNote\nThis course is held online via Zoom.\nReferences\nManfredo P. do Carmo, Differential Geometry of Curves and Surfaces, Dover Publications\nCourse contents\nSpheres The implicit function theorem The inverse function theorem Definition of regular surfaces Examples of regular surfaces The implicit function theorem and regular surfaces Surfaces of revolution End-of-term exam ","date":"5 octubre 2020","externalUrl":null,"permalink":"/lecture/2020w_geometryiia/","section":"Teaching","summary":"Term 3, Mon. Period 3 · Faculty of Science, Niigata University","title":"Geometry IIA","type":"lecture"},{"content":"For master\u0026rsquo;s students; Semester 1, intensive course · Graduate School of Science and Technology, Niigata University\nNote\nThis course is held online via Zoom.\nTextbooks\nY. Matsumoto, \u0026ldquo;多様体の基礎\u0026rdquo; (in Japanese), University of Tokyo Press I. Yokota, \u0026ldquo;多様体とモース理論\u0026rdquo; (in Japanese), Gendai-Sugakusha References\nJohn W. Milnor, Morse Theory, Princeton University Press Course contents\nWhat is Morse theory?; review of point-set topology (definitions, compactness, the Hausdorff property, continuous maps) Manifolds I (definition and examples of differentiable manifolds) Manifolds II ($C^{\\infty}$ functions, tangent spaces, $C^{\\infty}$ maps) Manifolds III (critical points, vector fields, integral curves, one-parameter transformation groups, Riemannian metrics) Some preliminaries from algebraic topology (homotopy equivalences, deformation retracts, CW complexes, spaces obtained by attaching cells) Morse theory ","date":"31 agosto 2020","externalUrl":null,"permalink":"/lecture/2020s_difftopom/","section":"Teaching","summary":"For master’s students; Semester 1, intensive course · Graduate School of Science and Technology, Niigata University","title":"Topics in Differential Topology","type":"lecture"},{"content":" Morimichi Kawasaki, Ryuma Orita\nCommunications in Contemporary Mathematics, vol. 23 (2021), no. 5, 2050047\n· Abstract # In this paper, we introduce the notion of pseudoheaviness of closed subsets of closed symplectic manifolds and prove the existence of pseudoheavy fibers of moment maps. In particular, we generalize Entov and Polterovich\u0026rsquo;s theorem, which ensures the existence of non-displaceable fibers. As its application, we provide a partial answer to a problem posed by them, which asks the existence of heavy fibers. Moreover, we obtain a family of singular Lagrangian submanifolds in $S^2\\times S^2$ with various rigidities.\n","date":"7 julio 2020","externalUrl":null,"permalink":"/publication/07-existence-of-pseudoheavy-fibers/","section":"Publications","summary":"Morimichi Kawasaki, Ryuma Orita — Communications in Contemporary Mathematics, vol. 23 (2021), no. 5, 2050047","title":"Existence of pseudoheavy fibers of moment maps","type":"publication"},{"content":"Term 2, Fri. Period 4 (co-taught) · Faculty of Science, Niigata University\nNote\nThese exercise sessions are held online via Zoom.\nTextbooks\nY. Takahashi and M. Kato, \u0026ldquo;微分積分概論 [新訂版]\u0026rdquo; (in Japanese), Saiensu-sha N. Innami, T. Tanaka, H. Kojima, and A. Hoshi, \u0026ldquo;要点明解 線形代数\u0026rdquo; (in Japanese), Baifukan ","date":"19 junio 2020","externalUrl":null,"permalink":"/lecture/2020s_kisoenshu_b/","section":"Teaching","summary":"Term 2, Fri. Period 4 (co-taught) · Faculty of Science, Niigata University","title":"Basic Exercises in Mathematics b","type":"lecture"},{"content":"Term 2, Mon. Period 3 \u0026amp; Thu. Period 2 · Faculty of Science, Niigata University\nNote\nThis course is held online via Zoom.\nReferences\nManfredo P. do Carmo, Differential Geometry of Curves and Surfaces, Dover Publications M. Kurita, \u0026ldquo;復刊 積分幾何学\u0026rdquo; (in Japanese), Kyoritsu Shuppan H. Kawasaki, \u0026ldquo;極値問題\u0026rdquo; (in Japanese), Yokohama Tosho Course contents\nHistory of the isoperimetric problem; an elementary-geometric \u0026ldquo;proof\u0026rdquo; (06-18) The isoperimetric inequality (a proof via calculus) (06-22) Coordinates on the set of lines in the plane; the measure of sets of lines (06-25) The Cauchy–Crofton formula (06-29) Applications of the Cauchy–Crofton formula (07-02) Coordinates on the set of positions in the plane; the measure of sets of positions (07-06) The isoperimetric inequality (a proof using sets of positions) (07-09) The isoperimetric inequality (Blaschke\u0026rsquo;s proof) (07-13) Poincaré\u0026rsquo;s formula for sets of positions (07-16) The area of the region bounded by parallel curves (07-20) The volume of tubes (07-23) The isoperimetric inequality (Santaló\u0026rsquo;s proof) (07-27) The fundamental problem of the calculus of variations (07-30) The brachistochrone problem (08-03) Constrained variational problems (08-06) The isoperimetric inequality (a proof via the calculus of variations); the inscribed rectangle problem (08-10) ","date":"18 junio 2020","externalUrl":null,"permalink":"/lecture/2020s_geometryib/","section":"Teaching","summary":"Term 2, Mon. Period 3 \u0026 Thu. Period 2 · Faculty of Science, Niigata University","title":"Geometry IB","type":"lecture"},{"content":"Term 1, Fri. Period 4 (co-taught) · Faculty of Science, Niigata University\nNote\nThese exercise sessions are held online via Zoom.\nTextbooks\nY. Takahashi and M. Kato, \u0026ldquo;微分積分概論 [新訂版]\u0026rdquo; (in Japanese), Saiensu-sha N. Innami, T. Tanaka, H. Kojima, and A. Hoshi, \u0026ldquo;要点明解 線形代数\u0026rdquo; (in Japanese), Baifukan ","date":"24 abril 2020","externalUrl":null,"permalink":"/lecture/2020s_kisoenshu_a/","section":"Teaching","summary":"Term 1, Fri. Period 4 (co-taught) · Faculty of Science, Niigata University","title":"Basic Exercises in Mathematics a","type":"lecture"},{"content":"Term 1, Mon. Period 3 \u0026amp; Thu. Period 2 · Faculty of Science, Niigata University\nNote\nThis course is held online via Zoom.\nReferences\nManfredo P. do Carmo, Differential Geometry of Curves and Surfaces, Dover Publications\nCourse contents\nParametrized differentiable curves; inner products (04-20) Exercises; quiz 1 (04-23) Regular curves; arc length; orientation of vector spaces; cross products (04-27) Exercises; quiz 2 (04-30) Properties of the cross product; curvature of curves; principal normal vectors (05-04) Exercises; quiz 3 (05-07) Binormal vectors; torsion; the Frenet–Serret formulas; radius of curvature (05-11) Exercises; quiz 4 (05-14) The fundamental theorem of space curves; local canonical form (05-18) Exercises; quiz 5 (05-21) The Jordan curve theorem; the rotation index of plane curves (05-25) Exercises; quiz 6 (05-28) The rotation index theorem; the four-vertex theorem (06-01) Exercises; quiz 7 (06-04) Proof of the four-vertex theorem (06-08) Exercises; quiz 8 (06-11) ","date":"20 abril 2020","externalUrl":null,"permalink":"/lecture/2020s_geometryia/","section":"Teaching","summary":"Term 1, Mon. Period 3 \u0026 Thu. Period 2 · Faculty of Science, Niigata University","title":"Geometry IA","type":"lecture"},{"content":"MSJ Spring Meeting 2020\nNihon University, Japan\nNote\nThis talk has been cancelled due to the uncertain situation of COVID-19 in Japan.\n","date":"16 marzo 2020","externalUrl":null,"permalink":"/talk/2020-03-msj/","section":"Talks","summary":"MSJ Spring Meeting 2020 · Nihon University, Japan","title":"Rigid fibers of spinning tops","type":"talk"},{"content":"Contact Structures, Singular Points, and Related Topics\nShizuoka, Japan\n","date":"23 enero 2020","externalUrl":null,"permalink":"/talk/2020-01-shizuoka/","section":"Talks","summary":"Contact Structures, Singular Points, and Related Topics · Shizuoka, Japan","title":"Rigid fibers of spinning tops","type":"talk"},{"content":" Ryuma Orita\nJournal of Symplectic Geometry, vol. 17 (2019), no. 6, pp. 1893–1927\n· Abstract # We show that the presence of a non-contractible one-periodic orbit of a Hamiltonian diffeomorphism of a connected closed symplectic manifold $(M,\\omega)$ implies the existence of infinitely many non-contractible simple periodic orbits, provided that the symplectic form $\\omega$ is aspherical and the fundamental group $\\pi_1(M)$ is either a virtually abelian group or an $\\mathrm{R}$-group. We also show that a similar statement holds for Hamiltonian diffeomorphisms of closed monotone or negative monotone symplectic manifolds under the same conditions on their fundamental groups. These results generalize some works by Ginzburg and Gürel. The proof uses the filtered Floer\u0026ndash;Novikov homology for non-contractible periodic orbits.\n","date":"17 enero 2020","externalUrl":null,"permalink":"/publication/04-on-the-existence-of-infinitely-many-non-contractible-periodic-orbits/","section":"Publications","summary":"Ryuma Orita — Journal of Symplectic Geometry, vol. 17 (2019), no. 6, pp. 1893–1927","title":"On the existence of infinitely many non-contractible periodic orbits of Hamiltonian diffeomorphisms of closed symplectic manifolds","type":"publication"},{"content":"International workshop on Geometry of Foliated Spaces\nRitsumeikan University, Japan\n","date":"30 noviembre 2019","externalUrl":null,"permalink":"/talk/2019-11-ritsumeikan/","section":"Talks","summary":"International workshop on Geometry of Foliated Spaces · Ritsumeikan University, Japan","title":"Rigid fibers of spinning tops","type":"talk"},{"content":"Part-time teaching assistant · College of Science and Engineering, Aoyama Gakuin University\n","date":"1 octubre 2019","externalUrl":null,"permalink":"/lecture/2019w/","section":"Teaching","summary":"Part-time teaching assistant · College of Science and Engineering, Aoyama Gakuin University","title":"Mathematical Sciences Laboratory II","type":"lecture"},{"content":"Geometry Seminar\nTohoku University, Japan\n","date":"25 junio 2019","externalUrl":null,"permalink":"/talk/2019-06-tohoku/","section":"Talks","summary":"Geometry Seminar · Tohoku University, Japan","title":"Existence of pseudo-heavy fibers of moment maps","type":"talk"},{"content":" Morimichi Kawasaki, Ryuma Orita\nJournal of Topology and Analysis, vol. 13 (2021), no. 2, pp. 443–468\n· Abstract # We present a lower bound for a fragmentation norm and construct a bi-Lipschitz embedding $I\\colon \\mathbb{R}^n\\to\\mathrm{Ham}(M)$ with respect to the fragmentation norm on the group $\\mathrm{Ham}(M)$ of Hamiltonian diffeomorphisms of a symplectic manifold $(M,\\omega)$. As an application, we provide an answer to Brandenbursky\u0026rsquo;s question on fragmentation norms on $\\mathrm{Ham}(\\Sigma_g)$, where $\\Sigma_g$ is a closed Riemannian surface of genus $g\\geq 2$.\n","date":"14 junio 2019","externalUrl":null,"permalink":"/publication/05-disjoint-superheavy-subsets/","section":"Publications","summary":"Morimichi Kawasaki, Ryuma Orita — Journal of Topology and Analysis, vol. 13 (2021), no. 2, pp. 443–468","title":"Disjoint superheavy subsets and fragmentation norms","type":"publication"},{"content":"Differential Topology Seminar\nKyoto University, Japan\n","date":"23 abril 2019","externalUrl":null,"permalink":"/talk/2019-04-kyoto/","section":"Talks","summary":"Differential Topology Seminar · Kyoto University, Japan","title":"Existence of pseudo-heavy fibers of moment maps","type":"talk"},{"content":"Part-time teaching assistant (biweekly) · College of Science and Engineering, Aoyama Gakuin University\n","date":"1 abril 2019","externalUrl":null,"permalink":"/lecture/2019s_analysis/","section":"Teaching","summary":"Part-time teaching assistant (biweekly) · College of Science and Engineering, Aoyama Gakuin University","title":"Exercises in Analysis II","type":"lecture"},{"content":"Part-time teaching assistant (biweekly) · College of Science and Engineering, Aoyama Gakuin University\n","date":"1 abril 2019","externalUrl":null,"permalink":"/lecture/2019s_ode/","section":"Teaching","summary":"Part-time teaching assistant (biweekly) · College of Science and Engineering, Aoyama Gakuin University","title":"Exercises in Differential Equations I","type":"lecture"},{"content":"Seminar\nSeoul National University, South Korea\n","date":"25 enero 2019","externalUrl":null,"permalink":"/talk/2019-01-snu/","section":"Talks","summary":"Seminar · Seoul National University, South Korea","title":"The number of fixed points of Hamiltonian diffeomorphisms","type":"talk"},{"content":"Seminar\nKorea Institute for Advanced Study (KIAS), South Korea\n","date":"22 enero 2019","externalUrl":null,"permalink":"/talk/2019-01-kias2/","section":"Talks","summary":"Seminar · Korea Institute for Advanced Study (KIAS), South Korea","title":"From Morse homology to Floer homology II","type":"talk"},{"content":"Seminar\nKorea Institute for Advanced Study (KIAS), South Korea\n","date":"21 enero 2019","externalUrl":null,"permalink":"/talk/2019-01-kias1/","section":"Talks","summary":"Seminar · Korea Institute for Advanced Study (KIAS), South Korea","title":"From Morse homology to Floer homology I","type":"talk"},{"content":"Topics on Lagrangian submanifolds and Hamiltonian dynamics\nChiba University, Japan\n","date":"13 julio 2018","externalUrl":null,"permalink":"/talk/2018-07-chiba2/","section":"Talks","summary":"Topics on Lagrangian submanifolds and Hamiltonian dynamics · Chiba University, Japan","title":"Periodic orbits of Hamiltonian systems and Floer theory II","type":"talk"},{"content":"Topics on Lagrangian submanifolds and Hamiltonian dynamics\nChiba University, Japan\n","date":"12 julio 2018","externalUrl":null,"permalink":"/talk/2018-07-chiba1/","section":"Talks","summary":"Topics on Lagrangian submanifolds and Hamiltonian dynamics · Chiba University, Japan","title":"Periodic orbits of Hamiltonian systems and Floer theory I","type":"talk"},{"content":" Morimichi Kawasaki, Ryuma Orita\nRIMS Kôkyûroku, vol. 2098 (2018), pp. 57–59\nJournal Page\nAbstract # We prove that a certain $C^0$-robust condition of a Hamiltonian function $H$ induces the existence of a point transported $\\varepsilon$ out of the original point by the Hamiltonian diffeomorphism $\\varphi_H$. Related to our observation, we provide a problem on Hamiltonian pseudo-rotations.\n","date":"8 junio 2018","externalUrl":null,"permalink":"/publication/06-application-of-fragmentation-norms/","section":"Publications","summary":"Morimichi Kawasaki, Ryuma Orita — RIMS Kôkyûroku, vol. 2098 (2018), pp. 57–59","title":"Application of fragmentation norms to transported points by Hamiltonian isotopies","type":"publication"},{"content":"Geometry Seminar\nTokyo Metropolitan University, Japan\n","date":"13 abril 2018","externalUrl":null,"permalink":"/talk/2018-04-tmu/","section":"Talks","summary":"Geometry Seminar · Tokyo Metropolitan University, Japan","title":"Disjoint superheavy subsets and fragmentation norms","type":"talk"},{"content":"Ryuma Orita\nTokyo Journal of Mathematics, vol. 41 (2018), no. 1, pp. 113–130\n· Abstract # In the present paper, we define Morse–Bott functions on manifolds with boundary which are generalizations of Morse functions and show Morse–Bott inequalities for these manifolds.\n","date":"18 diciembre 2017","externalUrl":null,"permalink":"/publication/01-morse-bott-inequalities/","section":"Publications","summary":"Ryuma Orita — Tokyo Journal of Mathematics, vol. 41 (2018), no. 1, pp. 113–130","title":"Morse-Bott inequalities for manifolds with boundary","type":"publication"},{"content":"15th Taiwan Geometry Symposium\nNational Tsing Hua University, Taiwan\n","date":"18 noviembre 2017","externalUrl":null,"permalink":"/talk/2017-11-nthu/","section":"Talks","summary":"15th Taiwan Geometry Symposium · National Tsing Hua University, Taiwan","title":"The number of fixed points of Hamiltonian diffeomorphisms","type":"talk"},{"content":"Seminar\nIBS Center for Geometry and Physics, South Korea\n","date":"8 noviembre 2017","externalUrl":null,"permalink":"/talk/2017-11-ibscgp/","section":"Talks","summary":"Seminar · IBS Center for Geometry and Physics, South Korea","title":"Asphericity, Eilenberg–MacLane spaces and periodic orbits in Hamiltonian dynamics","type":"talk"},{"content":"East Asian Symplectic Conference 2017\nSichuan University, China\n","date":"31 octubre 2017","externalUrl":null,"permalink":"/talk/2017-10-easc/","section":"Talks","summary":"East Asian Symplectic Conference 2017 · Sichuan University, China","title":"Asphericity and non-contractible periodic orbits in Hamiltonian dynamics","type":"talk"},{"content":"NCTS Differential Geometry Seminar\nNational Taiwan University, Taiwan\n","date":"21 septiembre 2017","externalUrl":null,"permalink":"/talk/2017-09-ncts/","section":"Talks","summary":"NCTS Differential Geometry Seminar · National Taiwan University, Taiwan","title":"Floer theory and non-contractible periodic orbits","type":"talk"},{"content":"64th Geometry Symposium\nKanazawa University, Japan\n","date":"30 agosto 2017","externalUrl":null,"permalink":"/talk/2017-08-kanazawa/","section":"Talks","summary":"64th Geometry Symposium · Kanazawa University, Japan","title":"Floer–Novikov theory and non-contractible periodic orbits","type":"talk"},{"content":"Hamiltonian and Reeb Dynamics, New Methods and Applications\nLorentz Center, The Netherlands\n","date":"21 julio 2017","externalUrl":null,"permalink":"/talk/2017-07-leiden/","section":"Talks","summary":"Hamiltonian and Reeb Dynamics, New Methods and Applications · Lorentz Center, The Netherlands","title":"On the existence of infinitely many non-contractible periodic orbits in Hamiltonian dynamics on closed symplectic manifolds","type":"talk"},{"content":"Topology Seminar\nGakushuin University, Japan\n","date":"14 julio 2017","externalUrl":null,"permalink":"/talk/2017-07-gakushuin/","section":"Talks","summary":"Topology Seminar · Gakushuin University, Japan","title":"Floer–Novikov theory and non-contractible periodic trajectories","type":"talk"},{"content":"Topology Seminar\nKyushu University, Japan\n","date":"19 mayo 2017","externalUrl":null,"permalink":"/talk/2017-05-kyushu/","section":"Talks","summary":"Topology Seminar · Kyushu University, Japan","title":"Floer–Novikov theory and non-contractible periodic trajectories","type":"talk"},{"content":"Ryuma Orita\nBulletin of the London Mathematical Society, vol. 49 (2017), no. 4, pp. 571–580\n· Abstract # We show that the presence of one non-degenerate, non-contractible periodic orbit of a Hamiltonian on the standard symplectic torus implies the existence of infinitely many simple non-contractible periodic orbits.\n","date":"21 abril 2017","externalUrl":null,"permalink":"/publication/03-non-contractible-periodic-orbits/","section":"Publications","summary":"Ryuma Orita — Bulletin of the London Mathematical Society, vol. 49 (2017), no. 4, pp. 571–580","title":"Non-contractible periodic orbits in Hamiltonian dynamics on tori","type":"publication"},{"content":" Morimichi Kawasaki, Ryuma Orita\nJournal of Modern Dynamics, vol. 11 (2017), pp. 313–339\n· Abstract # The first author introduced a relative symplectic capacity $C$ for a symplectic manifold $(N,\\omega_N)$ and its subset $X$ which measures the existence of non-contractible periodic trajectories of Hamiltonian isotopies on the product of $N$ with the annulus $A_R=(-R,R)\\times\\mathbb{R}/\\mathbb{Z}$. In the present paper, we give an exact computation of the capacity $C$ of the $2n$-torus $\\mathbb{T}^{2n}$ relative to a Lagrangian submanifold $\\mathbb{T}^n$ which implies the existence of non-contractible Hamiltonian periodic trajectories on $A_R\\times\\mathbb{T}^{2n}$. Moreover, we give a lower bound on the number of such trajectories.\n","date":"20 abril 2017","externalUrl":null,"permalink":"/publication/02-computation-of-annular-capacity/","section":"Publications","summary":"Morimichi Kawasaki, Ryuma Orita — Journal of Modern Dynamics, vol. 11 (2017), pp. 313–339","title":"Computation of annular capacity by Hamiltonian Floer theory of non-contractible periodic trajectories","type":"publication"},{"content":"Tuesday Seminar on Topology\nThe University of Tokyo, Japan\n","date":"24 enero 2017","externalUrl":null,"permalink":"/talk/2017-01-ut/","section":"Talks","summary":"Tuesday Seminar on Topology · The University of Tokyo, Japan","title":"On the existence of infinitely many non-contractible periodic trajectories in Hamiltonian dynamics on closed symplectic manifolds","type":"talk"},{"content":"Contact Structures, Singular Points, and Related Topics\nKanazawa University, Japan\n","date":"18 enero 2017","externalUrl":null,"permalink":"/talk/2017-01-kanazawa/","section":"Talks","summary":"Contact Structures, Singular Points, and Related Topics · Kanazawa University, Japan","title":"On the existence of infinitely many non-contractible periodic trajectories in Hamiltonian dynamics on closed symplectic manifolds","type":"talk"},{"content":"Teaching assistant · Faculty of Science, The University of Tokyo\nIndividual projects on topics of each student\u0026rsquo;s choice Writing an OS from scratch (following the book \u0026ldquo;OS自作入門\u0026rdquo;, in Japanese)\n","date":"1 octubre 2016","externalUrl":null,"permalink":"/lecture/2016w/","section":"Teaching","summary":"Teaching assistant · Faculty of Science, The University of Tokyo","title":"Computational Mathematics II","type":"lecture"},{"content":"Geometry Seminar\nTokyo Metropolitan University, Japan\n","date":"24 junio 2016","externalUrl":null,"permalink":"/talk/2016-06-tmu/","section":"Talks","summary":"Geometry Seminar · Tokyo Metropolitan University, Japan","title":"Non-contractible periodic orbits in Hamiltonian dynamics on tori","type":"talk"},{"content":"Workshop on Symplectic Geometry and Physics\nTohoku University, Japan\n","date":"25 mayo 2016","externalUrl":null,"permalink":"/talk/2016-05-tohoku/","section":"Talks","summary":"Workshop on Symplectic Geometry and Physics · Tohoku University, Japan","title":"Non-contractible periodic orbits in Hamiltonian dynamics on tori","type":"talk"},{"content":"Teaching assistant · Faculty of Science, The University of Tokyo\nPC hardware Mathematical software Basics of Unix/Linux Basics of programming System administration and information security ","date":"1 abril 2016","externalUrl":null,"permalink":"/lecture/2016s/","section":"Teaching","summary":"Teaching assistant · Faculty of Science, The University of Tokyo","title":"Computational Mathematics I","type":"lecture"},{"content":"Teaching assistant · Faculty of Science, The University of Tokyo\nIndividual projects on topics of each student\u0026rsquo;s choice Writing an OS from scratch (following the book \u0026ldquo;OS自作入門\u0026rdquo;, in Japanese)\n","date":"1 octubre 2015","externalUrl":null,"permalink":"/lecture/2015w/","section":"Teaching","summary":"Teaching assistant · Faculty of Science, The University of Tokyo","title":"Computational Mathematics II","type":"lecture"},{"content":"Teaching assistant · Faculty of Science, The University of Tokyo\nPC hardware Mathematical software Basics of Unix/Linux Basics of programming System administration and information security ","date":"1 abril 2015","externalUrl":null,"permalink":"/lecture/2015s/","section":"Teaching","summary":"Teaching assistant · Faculty of Science, The University of Tokyo","title":"Computational Mathematics I","type":"lecture"},{"content":"Teaching assistant · Faculty of Science, The University of Tokyo\nIndividual projects on topics of each student\u0026rsquo;s choice Building a server (a bulletin board supporting mathematical formulas)\n","date":"1 octubre 2014","externalUrl":null,"permalink":"/lecture/2014w/","section":"Teaching","summary":"Teaching assistant · Faculty of Science, The University of Tokyo","title":"Computational Mathematics II","type":"lecture"},{"content":"51st Topology Freshers\u0026rsquo; Seminar\nZaō, Miyagi, Japan\n","date":"23 julio 2014","externalUrl":null,"permalink":"/talk/2014-07-zao/","section":"Talks","summary":"51st Topology Freshers’ Seminar · Zaō, Miyagi, Japan","title":"Morse theory for manifolds with boundary","type":"talk"},{"content":"11th Kanto Young Geometers\u0026rsquo; Seminar\nWaseda University, Japan\n","date":"31 mayo 2014","externalUrl":null,"permalink":"/talk/2014-05-waseda/","section":"Talks","summary":"11th Kanto Young Geometers’ Seminar · Waseda University, Japan","title":"Morse–Bott inequalities for manifolds with boundary","type":"talk"},{"content":"Teaching assistant · Faculty of Science, The University of Tokyo\nPC hardware Mathematical software Basics of Unix/Linux Basics of programming System administration and information security ","date":"1 abril 2014","externalUrl":null,"permalink":"/lecture/2014s/","section":"Teaching","summary":"Teaching assistant · Faculty of Science, The University of Tokyo","title":"Computational Mathematics I","type":"lecture"},{"content":"Morse Theory and Related Topics\nKyoto University, Japan\n","date":"12 enero 2014","externalUrl":null,"permalink":"/talk/2014-01-kyoto/","section":"Talks","summary":"Morse Theory and Related Topics · Kyoto University, Japan","title":"Morse–Bott inequalities for manifolds with boundary","type":"talk"},{"content":"Teaching assistant · Faculty of Science, The University of Tokyo\nIndividual projects on topics of each student\u0026rsquo;s choice Writing an OS from scratch (following the book \u0026ldquo;OS自作入門\u0026rdquo;, in Japanese)\n","date":"1 octubre 2013","externalUrl":null,"permalink":"/lecture/2013w/","section":"Teaching","summary":"Teaching assistant · Faculty of Science, The University of Tokyo","title":"Computational Mathematics II","type":"lecture"},{"content":"Teaching assistant · Faculty of Science, The University of Tokyo\nPC hardware Mathematical software Basics of Unix/Linux Basics of programming System administration and information security ","date":"1 abril 2013","externalUrl":null,"permalink":"/lecture/2013s/","section":"Teaching","summary":"Teaching assistant · Faculty of Science, The University of Tokyo","title":"Computational Mathematics I","type":"lecture"},{"content":"49th Topology Freshers\u0026rsquo; Seminar\nKaratsu, Saga, Japan\n","date":"15 agosto 2012","externalUrl":null,"permalink":"/talk/2012-08-saga/","section":"Talks","summary":"49th Topology Freshers’ Seminar · Karatsu, Saga, Japan","title":"Applications of Morse Theory","type":"talk"},{"content":"Geometry and Transformation Groups 2012\nTambara Institute of Mathematical Sciences, The University of Tokyo, Japan\n","date":"27 julio 2012","externalUrl":null,"permalink":"/talk/2012-07-tambara/","section":"Talks","summary":"Geometry and Transformation Groups 2012 · Tambara Institute of Mathematical Sciences, The University of Tokyo, Japan","title":"Morse homology of Grassmann manifolds","type":"talk"},{"content":"Teaching assistant · College of Arts and Sciences, The University of Tokyo\n","date":"1 abril 2012","externalUrl":null,"permalink":"/lecture/2012/","section":"Teaching","summary":"Teaching assistant · College of Arts and Sciences, The University of Tokyo","title":"Mathematics IB","type":"lecture"},{"content":" Members (AY 2026) # D3 # KY: Algebraic topology and applications of Morse theory D2 # KY: Teichmüller space and the Thurston spine M2 # SY: Pseudo-Riemannian geometry and relativity CT: Morse homology M1 # SK, SO: Persistence theory B4 # SF HI: \u0026ldquo;手を動かしてまなぶ 集合と位相\u0026rdquo; by A. Fujioka (in Japanese) Theses # Kohei Yamada, \u0026ldquo;Eutaxy of generalized systoles\u0026rdquo; (in Japanese), Master\u0026rsquo;s thesis, AY 2024 Kanta Koeda, \u0026ldquo;Decompositions of Morse bipersistence modules into rectangles\u0026rdquo; (in Japanese), Master\u0026rsquo;s thesis, AY 2023 Kanon Yashiro, \u0026ldquo;Computing Morse-Bott homology with singular simplicial chains\u0026rdquo;, Master\u0026rsquo;s thesis, AY 2023 Yuki Yamamoto, \u0026ldquo;Existence of pseudoheavy fibers of proper moment maps\u0026rdquo; (in Japanese), Master\u0026rsquo;s thesis, AY 2023 Textbooks used in past senior seminars # Y. Matsumoto, \u0026ldquo;多様体の基礎\u0026rdquo; (in Japanese), University of Tokyo Press M. Masuda, \u0026ldquo;代数的トポロジー\u0026rdquo; (in Japanese), Asakura Shoten Allen Hatcher, \u0026ldquo;Algebraic Topology\u0026rdquo;, Cambridge University Press Loring W. Tu, \u0026ldquo;An Introduction to Manifolds\u0026rdquo;, Springer Y. Matsumoto, \u0026ldquo;Morse理論の基礎\u0026rdquo; (in Japanese), Iwanami Shoten A. Kawauchi, \u0026ldquo;結び目の理論\u0026rdquo; (in Japanese), Kyoritsu Shuppan Vladimir I. Arnold, \u0026ldquo;Mathematical Methods of Classical Mechanics\u0026rdquo;, Springer Joseph J. Rotman, \u0026ldquo;An Introduction to Algebraic Topology\u0026rdquo;, Springer John W. Milnor, \u0026ldquo;Morse Theory\u0026rdquo;, Princeton University Press Y. Ike, E. G. Escolar, I. Obayashi, and S. Kaji, \u0026ldquo;位相的データ解析から構造発見へ\u0026rdquo; (in Japanese), Saiensu-sha A. Fujioka, \u0026ldquo;手を動かしてまなぶ 集合と位相\u0026rdquo; (in Japanese), Shokabo ","externalUrl":null,"permalink":"/zemi/","section":"Ryuma ORITA","summary":"","title":"Research Group (Seminar)","type":"page"},{"content":"Soy profesor asociado en el Departamento de Matemáticas de la Universidad de Niigata. Mi investigación se centra en la dinámica hamiltoniana en geometría simpléctica.\nLíneas de investigación # Teoría de Morse y teoría de Floer Módulos de persistencia Complejidad topológica Formación y cargos # Periodo Cargo / Titulación Institución 2024.7 – Profesor asociado Universidad de Niigata 2020.3 – 2024.6 Profesor asistente Universidad de Niigata 2018.4 – 2020.2 Investigador JSPS (PD) Universidad Metropolitana de Tokio 2017.8 – 2018.3 Investigador posdoctoral Centro Nacional de Ciencias Teóricas (NCTS) 2017.3 Doctorado en ciencias matemáticas Universidad de Tokio 2014.4 – 2017.3 Investigador JSPS (DC1) Universidad de Tokio 2014.3 Máster en ciencias matemáticas Universidad de Tokio 2012.3 Grado en ciencias Universidad de Kyushu Las páginas detalladas (publicaciones, charlas, docencia) están disponibles en inglés y japonés.\n","externalUrl":null,"permalink":"/es/","section":"Ryuma ORITA","summary":"","title":"Ryuma ORITA","type":"page"}]