Shin HAYASHI's Home Page

About

I am an assistant professor(fixed term) in the Department of Physics and Mathematics at Aoyama Gakuin University. My research area includes K-theory, Atiyah-Singer index theorem. My current interest is an application of these theories to topological phases of matter.

Contact

shin.hayashi[at]math.aoyama.ac.jp

Papers

  1. Shin Hayashi, Bulk-edge correspondence and the cobordism invariance of the index, Rev. Math. Phys., 29(10), 1750033 (2017).
    published final version in RMP , (arXiv:1611.08073).
  2. Shin Hayashi, Topological invariants and corner states for Hamiltonians on a three-dimensional lattice, Commun. Math. Phys., 364(1), 343--356 (2018).
    published final version in CMP , (arXiv:1611.09680).
  3. Shin Hayashi, Toeplitz operators on concave corners and topologically protected corner states, Lett. Math. Phys., 109(10), 2223--2254 (2019).
    published final version in LMP , (arXiv:1902.01533).
  4. Ryo Okugawa, Shin Hayashi, Takeshi Nakanishi, Second-order topological phases protected by chiral symmetry, Phys. Rev. B, 100, 235302 (2019).
    published final version in PRB , (arXiv:1907.01153).
  5. Yuki Nagasato, Yoshitake Takane, Yukinori Yoshimura, Shin Hayashi, Takeshi Nakanishi, Gapless states localized along a staircase edge in second order topological insulators, J. Phys. Soc. Jpn., 90, 104703(2021).
    published final version in JPSJ , (arXiv:2109.06412).
  6. Shin Hayashi, Classification of topological invariants related to corner states, Lett. Math. Phys., 111, Article number:118(2021), online first.
    published final version in LMP , (arXiv:2102.12231).
  7. Shin Hayashi, An index theorem for quarter-plane Toeplitz operators via extended symbols and gapped invariants related to corner states, Commun. Math. Phys., 400, 429--462 (2023).
    published final version in CMP , (arXiv:2203.09117).

Proceedings

  1. Shin Hayashi, On some topological invariants related to localized wave functions, RIMS kokyuroku No.2052, 82--90, 2017. link

Preprints

  1. Shin Hayashi, Localization of Dirac operators on 4n+2 dimensional open spinc manifolds, arXiv:1306.0389.

Talks

  1. Atiyah-Singer index theorem and Dirac operators, Kansai low dimensional topology young seminar, Nara Women’s University, Nara, Oct. 2013.
  2. Localization of Dirac Operators on 4n+2 Dimensional Open Spinc Manifolds, Geometry seminar, Tokyo Institute of Technology, Tokyo, Nov.2013.
  3. Localization of Dirac Operators on 4n+2 Dimensional Open Spinc Manifolds, Geometry seminar, Osaka University, Osaka, Dec. 2013.
  4. Localization of Dirac Operators on 4n+2 Dimensional Open Spinc Manifolds, 61st Geometry Symposium, Meijo University, Aichi, Aug. 2014.
  5. Localization of Dirac Operators on 4n+2 Dimensional Open Spinc Manifolds and Its Applications, Friday Seminar on Knot Theory, Osaka City University, Osaka, Oct. 2014.
  6. Localization of Dirac Operators on 4n+2 Dimensional Open Spinc Manifolds and Its Applications, Geometry for Quantization 2014, Waseda University, Tokyo, Dec. 2014.
  7. K-Theoretic aspects on bulk-edge correspondence for topological insulators, Topology seminar (co-hosted by Mathematical Physics seminar), Shinshu University, Nagano, Jan. 2015.
  8. K-Theoretic aspects on bulk-edge correspondence for topological insulators, Young meeting on Noncommutative Geometry, Nagoya University, Aichi, Mar. 2015.
  9. Bordism invariance of indices and the bulk-edge correspondence, Mini-workshop on topological states and non-commutative geometry, Tohoku University AIMR, Miyagi, Mar. 2015.
  10. K-Theory and bulk-edge correspondence(two talks), Kagurazaka workshop "Topological insulators and K-theory", Tokyo University of Science, Tokyo, May. 2015.
  11. Topological Invariants and Corner States for Hamiltonians on a Three Dimensional Lattice, Tuesday Seminar on Topology, The University of Tokyo, Tokyo, Jan. 2017.
  12. Topological Invariants and Corner States for Hamiltonians on a Three Dimensional Lattice, Geometry seminar, Tohoku University, Miyagi, Apr. 2017.
  13. On some topological invariants related to localized wave functions, Intelligence of Low-dimensional Topology, RIMS, Kyoto, May 2017.
  14. Topological invariants for some codimension-two systems and its properties, "Variety and universality of bulk-edge correspondence in topological phases: From solid state physics to transdisciplinary concepts", Grant-in-Aid for Scientific Research (S), get together meeting, Tsukuba University, Tokyo, June 2017.
  15. Topological invariants and corner states for Hamiltonians on a three dimensional lattice, Mathematical aspects of topological phases of matter and quantum computing, Tohoku University AIMR, Miyagi, July 2017.
  16. On an explicit example of topologically protected corner states, Tuesday Seminar on Topology, The University of Tokyo, Tokyo, Nov. 2017.
  17. Bulk-edge and corner correspondence, International workshop "Variety and universality of bulk-edge correspondence in topological phases: From solid state physics to transdisciplinary concepts"(BEC2018), Tsukuba University, Ibaraki, Jan. 2018.
  18. Bulk-edge correspondence and the cobordism invariance of the index, MSJ Spring Meeting, The University of Tokyo, Tokyo, Mar. 2018.
  19. Bulk-edge and corner correspondence, MSJ Spring Meeting, The University of Tokyo, Tokyo, Mar. 2018.
  20. Gapped-gapless correspondence for systems with codimension-one or -two boundaries, Math group seminar, Tohoku University AIMR, Miyagi, Apr. 2018.
  21. Corner topological invariants and its variants, "Variety and universality of bulk-edge correspondence in topological phases: From solid state physics to transdisciplinary concepts", Tsukuba University, Ibaraki, May 2018.
  22. On some topological invariants related to corner states, Progress in the mathematics of topological states of matter, Tohoku University AIMR, Miyagi, Aug. 2018.
  23. Topological invariants and corner states for Hamiltonians on a three dimensional lattice, Topology and computer 2018, Nara Women's University, Nara, Oct. 2018.
  24. On some topological invariants related to corner states ~its definition and some properties~, Applied singularity theory lab seminar, Hokkaido University, Hokkaido, Jan. 2019.
  25. Index theory for Toeplitz operators associated with some concave corners and its applications, MSJ Spring Meeting, Tokyo Institute of Technology, Tokyo, Mar. 2019.
  26. Topological invariants and corner states, Topological Phases of Interacting Quantum Systems, Casa Matemática Oaxaca, Mexico, June 2019.
  27. Topological invariants and corner states for Hamiltonians on a lattice, Grant-in-Aid for Scientific Research on Innovative Areas "Discrete Geometric Analysis for Materials Design" research results presentation, Nagoya University, Aichi, Aug. 2019.
  28. Topological invariants and corner states for some Hamiltonians on a lattice, 66th Topology Symposium, Nigiwai Koryukan AU, Akita, Aug. 2019.
  29. Topological K-theory and the bulk-edge correspondence, Young mathematicians workshop on algebraic, geometric, and analytic aspects of K-theory and vector bundles, University of the Ryukyus, Okinawa, Aug. 2019.
  30. Index theory for some Toeplitz operators associated with some corners and its applications, 66th Geometry Symposium, Nagoya University, Aichi, Aug. 2019.
  31. On topologies for (higher-order) topological insulators, Kansai gauge theory seminar, Kyoto University, Kyoto, Oct. 2019.
  32. Topological invariants and corner states for Hamiltonians on a lattice, 13th Joint Research Meeting of MEXT National Projects on Condensed-Matter Science, The University of Tokyo, Tokyo, Nov. 2019.
  33. Topological invariants and corner states for Hamiltonians on a lattice, TMU Geometry Seminar, Tokyo Metropolitan University, Tokyo, Dec. 2019.
  34. Index theory for some Toeplitz operators and (higher-order) topological insulators, Kobe geometry seminar, Kobe University, Hyogo, Jan. 2020.
  35. A mathematical approach to higher-order topological insulators, Topological surface states, solitons, branes and index theorems, Osaka University, Osaka, Feb. 2020.
  36. Classification of topological invariants related to corner states, MSJ Spring Meeting, Keio University, Mar. 2021.
  37. Topological invariants and corner states for Hamiltonians on a lattice, The 27th Osaka City University International Academic Symposium "Mathematical Science of Visualization, and Deepening of Symmetry and Moduli", Osaka City University, Osaka, Mar. 2021. (short talk)
  38. On a topological invariant related to corner states via index theory and matrix factorizations, ”Variety and universality of bulk-edge correspondence in topological phases:From solid-state physics to transdisciplinary concepts" (BE/BC2022), Tsukuba University, Ibaraki, Feb. 2022.
  39. Topological invariants related to corner states via index theory and matrix factorizations, CREST Research Seminar on “Theoretical studies of topological phases of matter”, online, May. 2022.
  40. An index theoretic approach to topological corner states, JSIAM Annual Meeting, Hokkaido University (online), Sep. 2022.
  41. An index theorem for quarter-plane Toeplitz operators via extended symbols, MSJ Autumn Meeting, Hokkaido University, Sep. 2022.
  42. Index theory for quarter-plane Toeplitz operators and topological corner states, Math group seminar, Tohoku University AIMR, Miyagi, Oct. 2022.
  43. Index theory for quarter-plane Toeplitz operators and topological corner states, Japan-Netherlands Joint Seminar: Index Theory and Operator Algebras in Topological Physics, Tohoku University AIMR, Miyagi, Mar. 2023.
  44. An index theoretic approach to topological corner states, Emerging Platforms for Quantum Computing, Tohoku University AIMR, Miyagi, Apr. 2023.
  45. Index theory and topological corner states, CREST/PRESTO "Topology" Area Public Symposium Present and future of topological devices, JST, online, Oct. 2023.
  46. Index formula for quarter-plane Toeplitz operators via extended symbols, Tuesday Seminar on Topology, The University of Tokyo, Tokyo, Oct. 2023.
  47. Index theory for quarter-plane Toeplitz operators and its applications, Aoyama Math seminar, Aoyama Gakuin University, Kanagawa, Nov. 2023.
  48. Index theory for quarter-plane Toeplitz operators via extended symbols, Geometry seminar, Osaka University, Osaka, Jan. 2024.
  49. An index formula for quarter-plane Toeplitz operators via extended symbols, Topology seminar, Shinshu University, Nagano, Apr. 2024.

Poster Presentations

  1. Bulk-edge-corner correspondence, Research exchange meeting in different field / different industry for young researchers in mathematics and mathematical sciences, Meiji University, Tokyo, Nov. 2016. (Best poster Award)
  2. Bulk-edge-corner correspondence, Ensemble Workshop for Young Researchers in Tohoku University, Tohoku University, Miyagi, July 2017.
  3. Bulk-edge-corner correspondence, Novel Quantum States in Condensed Matter 2017, Kyoto University, Kyoto, Oct. 2017.
  4. Topological invariants for 2-D class AIII systems with corners ~an example and the 2-D Benalcazar-Bernevig-Hughes model~, International workshop “Variety and universality of bulk-edge correspondence in topological phases: From solid state physics to transdisciplinary concepts”(BEC2018X), Tsukuba University, Tokyo, Dec. 2018.
  5. Topological invariants and corner states for Hamiltonians on a three dimensional lattice, Session ``Young Mathematicians' Challenge'', JST, Tokyo, Mar. 2019.
  6. Topological invariants related to corner states, International conference on discrete geometric analysis for materials design, online, Sep. 2021.
  7. Index theoretic approach to topological corner states, MflP workshop, Meiji University, Apr. 2024.

CV

  • Dec. 1988, Born in Ishikawa, Japan
  • Apr. 2004 -- Mar. 2007, Nanao High School (Ishikawa Prefecture)
  • Apr. 2007 -- Mar. 2011, The University of Tokyo (B.Sc)
  • Apr. 2011 -- Mar. 2013, The University of Tokyo (M.Sc. Advisor : Professor Mikio Furuta)
  • Apr. 2013 -- Mar. 2017, The University of Tokyo (Ph.D. Advisor : Professor Mikio Furuta)
  • Apr. 2017 -- June 2021, Postdoc in AIST-TohokuU Mathematics for Advanced Materials Open Innovation Laboratory(MathAM-OIL)
  • Oct. 2019 -- June 2021, PRESTO Researcher in Japan Science and Technology Agency(JST)(Concurrent post)
  • June 2021 -- Mar. 2023, PRESTO Researcher in Japan Science and Technology Agency
  • June 2021 -- Mar. 2023, Assistant Professor in Advanced Institute for Materials Research(AIMR), Tohoku University (seconded from JST)
  • Apr. 2023 -- Aug. 2023, Assistant Professor in Advanced Institute for Materials Research, Tohoku University
  • Sep. 2023 -- (Current), Assistant Professor in Department of Physics and Mathematics, Aoyama Gakuin University

Foundings

  • Grant-in-Aid for Early-Career Scientists, KAKENHI, Japan Society for the Promotion of Science,
    Project Title: Geometric study of some higher-order topological invariants related to corners (principal investigator), Apr. 2019 – Mar. 2023
  • PRESTO-Sakigake, Japan Science and Technology, Project Area: Topological Materials Science for Creation of Innovative Functions,
    Project Title: Topological study of systems of various shape based on index theory (principal investigator), Oct. 2019 – Mar. 2023
    link : JST PRESTO
  • Grant-in-Aid for Early-Career Scientists, KAKENHI, Japan Society for the Promotion of Science,
    Project Title: Mathematical syudy of topologies for higher-order topological insulators (principal investigator), Apr. 2023 – Mar. 2028 (Scheduled)

Teaching Experience

  • Teaching Assistant, University of Tokyo, 2011 and 2013
    General Topology (2011), Calculus (2013)
  • Research Assistant, University of Tokyo, 2013-2014
    Calculus (2013), Linear Algebra (2014)
  • Aoyama Gakuin University, 2023-(Current)
    Math Exercise A/B, Geometry I Exercise, Geometry Ⅲ Exercise, Analysis ⅡB Exercise, Analysis III Exercise
  • Musashino University, 2024-(Current)
    Topology and its applications

Awards

  • Best poster award, in research exchange meeting in different field and different industry for young researchers in mathematics and mathematical sciences, 2016.

Professional Memberships

  • The Mathematical Society of Japan (Member #11791)

Other Activities

  • Organized 49th Topology Fresher's Seminar, Saga, 2012
  • Lecturer at NothJP(citizen group), 2013--2014
  • Talk at 2nd Science Front organized by 0to1 (Interdisciplinary exchange group at Tokyo university)
  • Advisor at 60th Topology Fresher's Seminar, Yamanashi, 2024