Index theorem and Topological surface state

• Project Area: Discrete Geometric Analysis for Materials Design
• Project/Area Number: 17H06461
• Research Category: Grant-in-Aid for Scientific Research on Innovative Areas (Research in a proposed research area)
• Allocation Type: Single-year Grants
• Review Section: Science and Engineering
• Research Institution: The University of Tokyo
• Principal Investigator: Furuta Mikio 東京大学, 大学院数理科学研究科, 教授 (50181459)
• Co-Investigator(Kenkyū-buntansha): 五味 清紀 東京工業大学, 理学院, 教授 (00543109) ; 加藤 毅 京都大学, 理学研究科, 教授 (20273427)
• Project Period (FY): 2017-06-30 – 2022-03-31
• Project Status: Completed (Fiscal Year 2021)
• Budget Amount: ¥52,130,000 (Direct Cost: ¥40,100,000、Indirect Cost: ¥12,030,000); Fiscal Year 2021: ¥11,700,000 (Direct Cost: ¥9,000,000、Indirect Cost: ¥2,700,000); Fiscal Year 2020: ¥11,700,000 (Direct Cost: ¥9,000,000、Indirect Cost: ¥2,700,000); Fiscal Year 2019: ¥11,700,000 (Direct Cost: ¥9,000,000、Indirect Cost: ¥2,700,000); Fiscal Year 2018: ¥11,700,000 (Direct Cost: ¥9,000,000、Indirect Cost: ¥2,700,000); Fiscal Year 2017: ¥5,330,000 (Direct Cost: ¥4,100,000、Indirect Cost: ¥1,230,000)
• Keywords: 指数定理 / バルクエッジ対応 / 格子指数定理 / ドメインウォール / トポロジー / Bott周期性 / K群 / スペクトル切断 / Wilson-Dirac作用素 / ゲージ理論

Outline of Final Research Achievements

Atiyah-Singer index theorem is a formula giving the index of linear elliptic PDE　on a closed manifold topologically. Our main results are (1) a proof of a new formulataion of Atiyah-Patodi-SInger index theorem for manifold with boundary, (2) a new approach to lattice index theorem based on the role of the Wilson we found for the Wilson-Dirac equation on lattices, and (3) a new proof of Bott periodicity theorem based on spectral section.

Academic Significance and Societal Importance of the Research Achievements

純粋数学と物性物理の研究の新らな橋渡しを数学者と物理学者たちとの共同研究で与えた。
（１）4次元的現象が、4次元時空が平坦ではなく境界を持つ場合に物理的な考察と計算に基づいて与えられていた。当研究では4次元的対象を5次元空間に埋め込み、4次元の物理を5次元の幾何学から俯瞰することにより数学的な解明を与えた。
（２）相対論的量子力学のDirac方程式に対しては、格子近似は特有の項（Wilson項）を導入して行われている。今回の研究ではWilson項が数学的に果たす役割を明らにし、この20年進展のなかったパラメータ付のDirac方程式に対しても近似可能であると示した。

Research Products

• [Journal Article] The Cohomology Invariant for Class DIII Topological Insulators (2022)
  • Author(s): De Nittis Giuseppe、Gomi Kyonori
  • Journal Title: Annales Henri Poincare Volume: - Issue: 10 Pages: 3587-3632
  • DOI: 10.1007/s00023-022-01183-z
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] The Index Theorem of Lattice Wilson?Dirac Operators via Higher Index Theory (2022)
  • Author(s): Kubota Yosuke
  • Journal Title: Annales Henri Poincar? Volume: 23 Issue: 4 Pages: 1297-1319
  • DOI: 10.1007/s00023-022-01159-z
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] The relative Mishchenko-Fomenko higher index and almost flat bundles II: Almost flat index pairing (2022)
  • Author(s): Kubota Yosuke
  • Journal Title: Journal of Noncommutative Geometry Volume: 16 Issue: 1 Pages: 215-264
  • DOI: 10.4171/jncg/432
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Constraints on families of smooth 4-manifolds from Pin^-(2) -monopole (2022)
  • Author(s): Konno Hokuto, Nakamura Nobuhiro
  • Journal Title: Algebraic & Geometric Topology Volume: to appear
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] A note on the Nielsen realization problem for K3 surfaces (2022)
  • Author(s): David Baraglia, Konno Hokuto
  • Journal Title: Proceedings of the American Mathematical Society Volume: to appear
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] On the Bauer-Furuta and Seiberg-Witten invariants of families of 4‐manifolds (2022)
  • Author(s): Baraglia David、Konno Hokuto
  • Journal Title: Journal of Topology Volume: 15 Issue: 2 Pages: 505-586
  • DOI: 10.1112/topo.12229
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] A cohomological Seiberg?Witten invariant emerging from the adjunction inequality (2022)
  • Author(s): Konno Hokuto
  • Journal Title: Journal of Topology Volume: 15 Issue: 1 Pages: 108-167
  • DOI: 10.1112/topo.12215
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Seifert hypersurfaces of 2-knots and Chern?Simons functional (2022)
  • Author(s): Taniguchi Masaki
  • Journal Title: Quantum Topology Volume: 13 Issue: 2 Pages: 335-405
  • DOI: 10.4171/qt/165
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Hilbert bundles with ends (2021)
  • Author(s): Kato Tsuyoshi、Kishimoto Daisuke、Tsutaya Mitsunobu
  • Journal Title: Journal of Topology and Analysis Volume: - Issue: 02 Pages: 1-32
  • DOI: 10.1142/s1793525321500680
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] L 2 harmonic theory, Seiberg-Witten theory and asymptotics of differential forms (2021)
  • Author(s): Kato Tsuyoshi
  • Journal Title: Journal of Gokova Geometry Topology Volume: 15 Pages: 1-22
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Covering-monopole map and higher degree in non-commutative geometry (2021)
  • Author(s): Kato Tsuyoshi
  • Journal Title: Journal of Noncommutative Geometry Volume: 15 Issue: 3 Pages: 995-1071
  • DOI: 10.4171/jncg/430
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Induced map on K-theory for certain $\Gamma$-equivariant maps between Hilbert spaces (2021)
  • Author(s): Kato Tsuyoshi
  • Journal Title: Journal of Noncommutative Geometry Volume: 15 Issue: 4 Pages: 1433-1467
  • DOI: 10.4171/jncg/442
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Rigidity of the mod 2 families Seiberg-Witten invariants and topology of families of spin 4-manifolds (2021)
  • Author(s): Tsuyoshi Kato , Hokuto Konno and Nobuhiro Nakamura
  • Journal Title: Compositio Mathematica Volume: 157 Issue: 4 Pages: 770-808
  • DOI: 10.1112/s0010437x2000771x
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Homotopy Type of the Unitary Group of the Uniform Roe Algebra on ?n (2021)
  • Author(s): Kato Tsuyoshi, Kishimoto Daisuke, Tsutaya Mitsunobu
  • Journal Title: Journal of Topology and Analysis Volume: - Issue: 02 Pages: 1-18
  • DOI: 10.1142/s1793525321500357
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] ‘Real’ Gerbes and Dirac Cones of Topological Insulators (2021)
  • Author(s): Gomi Kiyonori、Thiang Guo Chuan
  • Journal Title: Communications in Mathematical Physics Volume: 388 Issue: 3 Pages: 1507-1555
  • DOI: 10.1007/s00220-021-04238-0
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Twisted crystallographic T-duality via the Baum-Connes isomorphism (2021)
  • Author(s): Gomi Kiyonori、Kubota Yosuke、Thiang Guo Chuan
  • Journal Title: International Journal of Mathematics Volume: 32 Issue: 10 Pages: 2150078-2150078
  • DOI: 10.1142/s0129167x21500786
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Classification of topological invariants related to corner states (2021)
  • Author(s): Hayashi Shin
  • Journal Title: Letters in Mathematical Physics Volume: 111 Issue: 5 Pages: 1-54
  • DOI: 10.1007/s11005-021-01460-8
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Gapless States Localized along a Staircase Edge in Second-Order Topological Insulators (2021)
  • Author(s): Nagasato Yuki、Takane Yositake、Yoshimura Yukinori、Hayashi Shin、Nakanishi Takeshi
  • Journal Title: Journal of the Physical Society of Japan Volume: 90 Issue: 10 Pages: 104703-104703
  • DOI: 10.7566/jpsj.90.104703
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] The bulk-dislocation correspondence for weak topological insulators on screw?dislocated lattices (2021)
  • Author(s): Kubota Yosuke
  • Journal Title: Journal of Physics A: Mathematical and Theoretical Volume: 54 Issue: 36 Pages: 364001-364001
  • DOI: 10.1088/1751-8121/ac190c
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] The Gromov?Lawson codimension 2 obstructionto positive scalar curvature and the C??index (2021)
  • Author(s): Kubota Yosuke、Schick Thomas
  • Journal Title: Geometry & Topology Volume: 25 Issue: 2 Pages: 949-960
  • DOI: 10.2140/gt.2021.25.949
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Characteristic classes via 4-dimensional gauge theory (2021)
  • Author(s): Hokuto Konno
  • Journal Title: Geometry & Topology Volume: 25 Issue: 2 Pages: 711-773
  • DOI: 10.2140/gt.2021.25.711
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Seiberg-Witten Floer Homotopy Contact Invariant (2021)
  • Author(s): Iida Nobuo, Taniguchi Masaki
  • Journal Title: Studia Scientiarum Mathematicarum Hungarica Volume: 58 Issue: 4 Pages: 505-558
  • DOI: 10.1556/012.2021.01511
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Homological bulk-edge correspondence for Weyl semimetal (2021)
  • Author(s): Kiyonori Gomi
  • Journal Title: Progress of Theoretical and Experimental Physics Volume: 0 Issue: 4 Pages: 0-0
  • DOI: 10.1093/ptep/ptab035
  • Peer Reviewed / Open Access
• [Journal Article] The simple type conjecture for mod 2 Seiberg-Witten invariants (2021)
  • Author(s): Kato Tsuyoshi、 Nakamura Nobuhiro、 Yasui Koichi
  • Journal Title: Journal of the European Mathematical Society Volume: -
  • Peer Reviewed
• [Journal Article] Freed-Moore K-theory (2021)
  • Author(s): Kiyonori Gomi
  • Journal Title: Communications in Analysis and Geometry Volume: -
  • Peer Reviewed
• [Journal Article] A note on the Nielsen realization problem for K3 surfaces (2021)
  • Author(s): David Baraglia, Hokuto Konno
  • Journal Title: Proceedings of the American Mathematical Society Volume: - Pages: 4079-4087
  • DOI: 10.1090/proc/15544
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Kitaev’s Stabilizer Code and Chain Complex Theory of Bicommutative Hopf Algebras (2021)
  • Author(s): Kim Minkyu
  • Journal Title: Communications in Mathematical Physics Volume: -
  • Peer Reviewed
• [Journal Article] The Atiyah-Patodi-Singer Index and Domain-Wall Fermion Dirac Operators (2020)
  • Author(s): H. Fukaya, M. Furuta, S. Matsuo, T. Onogi, S. Yamaguchi and M. Yamashita
  • Journal Title: Communicatios in Mathematical Physics Volume: 380 Issue: 3 Pages: 1295-1311
  • DOI: 10.1007/s00220-020-03806-0
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Smoothness filtration of the magnitude complex (2020)
  • Author(s): Gomi Kiyonori
  • Journal Title: Forum Mathematicum Volume: 32 Issue: 3 Pages: 625-639
  • DOI: 10.1515/forum-2019-0091
  • Peer Reviewed
• [Journal Article] Eigenvalue crossings in Floquet topological systems (2020)
  • Author(s): Gomi Kiyonori、Tauber Clement
  • Journal Title: Letters in Mathematical Physics Volume: 110 Issue: 3 Pages: 465-500
  • DOI: 10.1007/s11005-019-01225-4
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] The Geometry of (non-Abelian) Landau levels (2020)
  • Author(s): Giuseppe De Nittis, Kiyonori Gomi, Massimo Moscolari
  • Journal Title: Journal of Geometry and Physics Volume: 152 Pages: 103649-103649
  • DOI: 10.1016/j.geomphys.2020.103649
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Positive scalar curvature and 10/8-type inequalities on 4-manifolds with periodic ends (2020)
  • Author(s): Hokuto Konno, Masaki Taniguchi
  • Journal Title: Inventiones Mathematicae Volume: 222 Issue: 3 Pages: 833-880
  • DOI: 10.1007/s00222-020-00979-2
  • Peer Reviewed
• [Journal Article] On the K-theoretic classification of dynamically stable systems (2019)
  • Author(s): Giuseppe De Nittis, Kiyonori Gomi
  • Journal Title: Reviews in Mathematical Physics Volume: 31 Issue: 01 Pages: 1950003-1950003
  • DOI: 10.1142/s0129055x1950003x
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Crystallographic bulk-edge correspondence: glide reflections and twisted mod 2 indices (2019)
  • Author(s): Kiyonori Gomi,Guo Chuan Thiang
  • Journal Title: Letters in Mathematical Physics Volume: 109 Issue: 4 Pages: 857-904
  • DOI: 10.1007/s11005-018-1129-1
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Crystallographic T-duality (2019)
  • Author(s): Kiyonori Gomi,Guo Chuan Thiang
  • Journal Title: Journal of Geometry and Physics Volume: 139 Pages: 50-77
  • DOI: 10.1016/j.geomphys.2019.01.002
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Second-order topological phases protected by chiral symmetry (2019)
  • Author(s): Okugawa Ryo、Hayashi Shin、Nakanishi Takeshi
  • Journal Title: Physical Review B Volume: 100 Issue: 23 Pages: 205302-205302
  • DOI: 10.1103/physrevb.100.235302
  • Peer Reviewed
• [Journal Article] Toeplitz operators on concave corners and topologically protected corner states (2019)
  • Author(s): Hayashi Shin
  • Journal Title: Letters in Mathematical Physics Volume: 109 Issue: 10 Pages: 2223-2254
  • DOI: 10.1007/s11005-019-01184-w
  • Peer Reviewed
• [Journal Article] Chiral vector bundles (2018)
  • Author(s): Giuseppe De Nittis, Kiyonori Gomi
  • Journal Title: Mathematische Zeitschrift Volume: 290 Issue: 3-4 Pages: 775-830
  • DOI: 10.1007/s00209-018-2041-1
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Topological Invariants and Corner States for Hamiltonians on a Three-Dimensional Lattice (2018)
  • Author(s): Hayashi Shin
  • Journal Title: Communications in Mathematical Physics Volume: 364 Issue: 1 Pages: 343-356
  • DOI: 10.1007/s00220-018-3229-2
  • Peer Reviewed
• [Journal Article] Many-body topological invariants for fermionic short-range entangled topological phases protected by antiunitary symmetries (2018)
  • Author(s): Ken Shiozaki, Hassan Shapourian, Kiyonori Gomi, Shinsei Ryu
  • Journal Title: PHYSICAL REVIEW B Volume: 98 Issue: 3
  • DOI: 10.1103/physrevb.98.035151
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] The cohomological nature of the Fu-Kane-Mele invariant (2018)
  • Author(s): Guseppe De Nittis, Kiyonori Gomi
  • Journal Title: Journal of Geometry and Physics Volume: 124 Pages: 124-164
  • DOI: 10.1016/j.geomphys.2017.10.007
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] The FKMM-invariant in low dimension (2017)
  • Author(s): De Nittis Giuseppe、Gomi Kiyonori
  • Journal Title: Letters in Mathematical Physics Volume: 108 Issue: 5 Pages: 1225-1277
  • DOI: 10.1007/s11005-017-1029-9
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Fu-Kane-Mele monopoles in semimetals (2017)
  • Author(s): Guo Chuan Thiang, Koji Sato and Kiyonori Gomi
  • Journal Title: Nuclear Physics. B Volume: 923 Pages: 107-125
  • DOI: 10.1016/j.nuclphysb.2017.07.018
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Twists on the torus equivariant under the 2-dimensional crystallographic point groups (2017)
  • Author(s): Kiyonori Gomi
  • Journal Title: SIGMA. Symmetry, Integrability and Geometry. Methods and Applications. Volume: 13 Pages: 014-051
  • DOI: 10.3842/sigma.2017.014
  • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] A class of asymmetric gapped Hamiltonians on quantum spin chains and its characterization III (2017)
  • Author(s): Yoshiko Ogata
  • Journal Title: Comm. Math.Phys. Volume: 352 Issue: 3 Pages: 1205-1263
  • DOI: 10.1007/s00220-016-2810-9
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Bulk-edge correspondence and the cobordism invariance of the index (2017)
  • Author(s): Hayashi Shin
  • Journal Title: Reviews in Mathematical Physics Volume: 29 Issue: 10 Pages: 1750033-1750033
  • DOI: 10.1142/s0129055x17500337
  • Peer Reviewed / Int'l Joint Research
• [Presentation] On a topological invariant related to corner states via index theory and matrix factorizations (2022)
  • Author(s): Hayashi Shin
  • Organizer: ”Variety and universality of bulk-edge correspondence in topological phases:From solid-state physics to transdisciplinary concepts" (BE/BC2022), Tsukuba University, Ibaraki
  • Int'l Joint Research / Invited
• [Presentation] Homological bulk-edge correspondence for Weyl semimetal (2021)
  • Author(s): Gomi Kiyonori
  • Organizer: Topological Phases of Matter, Leysin, Switzerland (attended online)
  • Int'l Joint Research / Invited
• [Presentation] Homological bulk-edge correspondence for Weyl semimetal (2021)
  • Author(s): Gomi Kiyonori
  • Organizer: Internatinal Conference on Discrete Geometric Analysis for Materials Design, , online
  • Int'l Joint Research / Invited
• [Presentation] Weyl 半金属に対するホモロジー的バルク境界対応 (2021)
  • Author(s): 五味清紀
  • Organizer: ポアソン幾何とその周辺21
  • Int'l Joint Research / Invited
• [Presentation] The bulk-dislocation correspondence: an operator-algebraic approach (2021)
  • Author(s): Kubota Yosuke
  • Organizer: The 21st International Conference on Discrete Geometric Analysis for Materials Design
  • Int'l Joint Research / Invited
• [Presentation] The bulk-dislocation correspondence: an operator-algebraic approach (2021)
  • Author(s): Kubota Yosuke
  • Organizer: Topological phases of matter, Leysin, Switzerland (attended online)
  • Int'l Joint Research / Invited
• [Presentation] 同変K理論によるバンド絶縁体の分類 (2021)
  • Author(s): 五味 清紀
  • Organizer: オンラインCREST チュートリアル・ワークショップ 物質のトポロジカル相の理論的探究
  • Invited
• [Presentation] Topological invariants and corner states for Hamiltonians on a lattice (2021)
  • Author(s): 林 晋
  • Organizer: 第27回大阪市立大学国際学術シンポジウム 可視化の数理と対称性およびモジュライの深化
  • Invited
• [Presentation] トーラス上のDirac作用素の正方格子による有限次元近似 (2020)
  • Author(s): 古田幹雄
  • Organizer: Summer School 数理物理 2020
  • Invited
• [Presentation] L^2 harmonic theory and Seiberg-Witten・Bauer-Furuta theory on non-compact complete Riemannian 4-manifolds (2020)
  • Author(s): Kato Tsuyoshi
  • Organizer: The Eighth Pacific Rim Conference in Mathematics, Session on Differential Geometry
  • Int'l Joint Research / Invited
• [Presentation] L^2 harmonic theory and Seiberg-Witten・Bauer-Furuta theory on non-compact complete Riemannian 4-manifolds (2020)
  • Author(s): Kato Tsuyoshi
  • Organizer: SouthamptonKyoto Workshop 2
  • Int'l Joint Research / Invited
• [Presentation] A mathematical approach to higher-order topological insulators (2020)
  • Author(s): 林 晋
  • Organizer: トポロジカル表面状態、ソリトンとブレーン、指数定理
  • Invited
• [Presentation] Toeplitz作用素の指数理論と(高次)トポロジカル絶縁体のトポロジーについて (2020)
  • Author(s): 林 晋
  • Organizer: 神戸幾何学セミナー, 神戸大学
  • Invited
• [Presentation] Index of the Wilson-Dirac operator revisited: a discrete version of Dirac operator on a finite lattice (2020)
  • Author(s): 古田 幹雄
  • Organizer: 理研 iTHEMS Math Seminar
  • Invited
• [Presentation] The Atiyah-Patodi-Singer index theorem and domain walls (2019)
  • Author(s): Furuta Mikio
  • Organizer: MATERIALS 56 RESEARCH MEETING 2019 Materials Innovation for Sustainable Development Goals, YOKOHAMA SYMPOSIA
  • Int'l Joint Research / Invited
• [Presentation] The Atiyah-Patodi-Singer index theorem and domain walls (2019)
  • Author(s): Furuta Mikio
  • Organizer: International Molecule-type Workshop Frontiers in Lattice QCD and related topics, Yukawa Institute for Theoretical Physics, Kyoto University
  • Int'l Joint Research / Invited
• [Presentation] Seiberg-Witten 理論周辺の応用と発展 (2019)
  • Author(s): 加藤毅
  • Organizer: 第６６回幾何学シンポジウム
  • Invited
• [Presentation] A rigidity theorem of the Z_2-valued Seiberg-Witten invariants for spin families (2019)
  • Author(s): Kato Tsuyoshi
  • Organizer: Index Theory, Duality and Related FieldsIn honour of Varghese Mathai’s 60th birthday
  • Int'l Joint Research / Invited
• [Presentation] Twisted Donaldson invariant (2019)
  • Author(s): Kato Tsuyoshi
  • Organizer: K-theory and Noncommutative Geometry
  • Int'l Joint Research / Invited
• [Presentation] Topological Phases of Interacting Quantum Systems (2019)
  • Author(s): Gomi Kiyonori
  • Organizer: Casa Matematica Oaxaca, Mexico
  • Int'l Joint Research / Invited
• [Presentation] Topological phase and generalized (co)homology (2019)
  • Author(s): Gomi Kiyonori
  • Organizer: Rigorous Statistical Mechanics and Related Topics, Kyoto University
  • Int'l Joint Research / Invited
• [Presentation] Topological invariants and corner states for Hamiltonians on a lattice (2019)
  • Author(s): 林 晋
  • Organizer: 第６６回トポロジーシンポジウム
  • Invited
• [Presentation] ある種の角に対するテープリッツ作用素の指数理論とその応用 (2019)
  • Author(s): 林 晋
  • Organizer: 第６６回幾何学シンポジウム
  • Invited
• [Presentation] Topological phases of interacting quantum systems (2019)
  • Author(s): Hayashi Shin
  • Organizer: Casa Matematica Oaxaca, Mexico
  • Int'l Joint Research / Invited
• [Presentation] The Atiyah-Patodi-Singer index theorem and domain walls (2018)
  • Author(s): 古田幹雄
  • Organizer: BEC2018X Variety and universality of bulk-edge correspondence in topological phases: From solid state physics to transdisciplinary concepts, Tsukuba University
  • Int'l Joint Research / Invited
• [Presentation] Topological invariants andcorner states for Hamiltonians on a three dimensional lattice (2018)
  • Author(s): 林晋
  • Organizer: Topology and computer 2018, Nara Women’s University
  • Int'l Joint Research / Invited
• [Presentation] Twisted Donaldson invariant (2018)
  • Author(s): 加藤毅
  • Organizer: Gauge Theory and Applications, Universität Regensburg
  • Int'l Joint Research / Invited
• [Presentation] Asymptotic volume growth of the instanton moduli spaces over the four-sphere (2018)
  • Author(s): 松尾信一郎
  • Organizer: Gauge theory and applications at Universität Regensburg
  • Int'l Joint Research / Invited
• [Presentation] Band topology and submanifolds of matrices (2018)
  • Author(s): 五味清紀
  • Organizer: Recent progress in mathematics of topological insulators, ETH Zürich, Switzerland
  • Int'l Joint Research / Invited
• [Presentation] Twisted Donaldson invariant (2018)
  • Author(s): 加藤毅
  • Organizer: Gauge Theory in Fukuoka
  • Int'l Joint Research / Invited
• [Presentation] Relative higher index and almost flat bundles (2018)
  • Author(s): 窪田陽介
  • Organizer: Gauge Theory in Fukuoka
  • Int'l Joint Research / Invited
• [Presentation] A (3+1)-dimensional TQFT with TRS-like symmetry (2018)
  • Author(s): 古田幹雄
  • Organizer: Variety and universality of bulk-edge correspondence in topological phases, University of Tsukuba
  • Int'l Joint Research / Invited
• [Presentation] Topological crystalline insulators and K-theory (2018)
  • Author(s): 五味清紀
  • Organizer: Topology & Condensed Matter , National Tsing Hua University, Taiwan, March 22-23
  • Int'l Joint Research / Invited
• [Presentation] Pin(2)-Seiberg-Witten Floer functor on homology 3-spheres (2017)
  • Author(s): 古田幹雄
  • Organizer: Mathematical Aspects of Topological Phases of Matter and Quantum Computing, AIMR
  • Int'l Joint Research / Invited
• [Presentation] A class of asymmetric gapped Hamiltonians on quantum spin (2017)
  • Author(s): 緒方芳子
  • Organizer: "Operator algebras and Quantum Information Theory", IHP Paris
  • Int'l Joint Research / Invited
• [Remarks] A01「トポロジカル物質」
  • URL: https://www.math-materials.jp/outline/#a01
• [Remarks] 研究成果報告書
  • URL: https://www.ms.u-tokyo.ac.jp/activity/annualreport.html
• [Remarks] 研究成果報告書 令和元年度 東京大学大学院数理科学研究科
  • URL: https://www.ms.u-tokyo.ac.jp/activity/documents/AnnualReport2019.pdf
• [Remarks] 東大数理： 研究成果報告書平成30年度
  • URL: https://www.ms.u-tokyo.ac.jp/activity/documents/AnnualReport2018.pdf
• [Remarks] 京都大学 教育研究活動データベース
  • URL: https://kyouindb.iimc.kyoto-u.ac.jp/j/cA2iC
• [Remarks] Kiyonori Gomi's Website
  • URL: http://www.math.titech.ac.jp/~kgomi/
• [Funded Workshop] PROGRESS IN THE MATHEMATICS OF TOPOLOGICAL STATES OF MATTER, AIMR (2019)
• [Funded Workshop] Topology and Computer 2018, Oct. 12 (Fri) - 14 (Sun) around midday Venue: Nara Women’s University, Collaboration Center Z306 (2018)
• [Funded Workshop] Symposium on Transformation Groups, Kumamoto City International Center,December 6(Thu) - December 8(Sat), 2018 (2018)
• [Funded Workshop] East Asian Conference on Gauge theory and Related Topics, Kyoto university, September 11- September 15, 2018 (2018)
• [Funded Workshop] Gauge Theory in Fukuoka (2018)