Shin HAYASHI's Home Page


About

I am a postdoctoral researcher at Mathematics for Advanced Materials-OIL(MathAM-OIL), AIST c/o AIMR, Tohoku 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]aist.go.jp


Papers/論文

  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, Comm. 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).

Proceedings/講究録

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

Preprints/プレプリント

  1. Shin Hayashi, Localization of Dirac operators on 4n+2 dimensional open spin^c manifolds, arXiv:1306.0389.
  2. Ryo Okugawa, Shin Hayashi, Takeshi Nakanishi, Second-order topological phases protected by chiral symmetry, arXiv:1907.01153.

Talks/講演

  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 Spin^c Manifolds, Geometry seminar, Tokyo Institute of Technology, Tokyo, Nov.2013.
  3. Localization of Dirac Operators on 4n+2 Dimensional Open Spin^c Manifolds, Geometry seminar, Osaka University, Osaka, Des. 2013.
  4. Localization of Dirac Operators on 4n+2 Dimensional Open Spin^c Manifolds, 61st Geometry Symposium, Meijo University, Aichi, Aug. 2014.
  5. Localization of Dirac Operators on 4n+2 Dimensional Open Spin^c 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 Spin^c Manifolds and Its Applications, Geometry for Quantization 2014, Waseda University, Tokyo, Des. 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, Tokyo University, 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, Tokyo University, 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 Meething, 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.

Poster Presentations/ポスター発表

  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.

CV/略歴

  • Des. 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 -- Postdoc in AIST-TohokuU Mathematics for Advanced Materials-OIL

Foundings/競争的資金:

  • 日本学術振興会科研費(若手研究)「コーナーに関連したある種の高次不変量の幾何学的研究」, 平成31年度--令和4年度, 課題番号19K14545

Professional Societies/所属学会

  • The Mathematical Society of Japan (Member #11791)

Teaching/職歴

TA・RA

  • 2011年度冬学期, 集合と位相演習, 古田幹雄先生
  • 2013年度夏学期, 数学1A, 逆井卓也先生
  • 2013年度冬学期, 数学1A, 逆井卓也先生
  • 2014年度冬学期. 数学2演習, 金井政宏先生

Outreach/アウトリーチ活動等

  • 第49回トポロジー新人セミナー幹事, 2012
  • NothJPで「放課後の数学」を開講, 2013--2014
  • 0to1 東大理学系・分野間交流グループ主催の第2回Science Frontで講演, 2013