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2016 Fiscal Year Annual Research Report

Probing crystal defects with scattering theory and non-commutative topology

Research Project

Project/Area Number 26707005
Research InstitutionNagoya University

Principal Investigator

Richard Serge  名古屋大学, 多元数理科学研究科(国際), G30特任教授 (70725241)

Project Period (FY) 2014-04-01 – 2017-03-31
Keywordsspectral theory / scattering theory / wave operators / index theorem / quantum walk
Outline of Annual Research Achievements

During this last year of the project, a second joint paper with my PhD student has been submitted for publication in July 2016. In September we traveled in France and delivered several talks. A collaboration with F. Nicoleau (Nantes) has started during this trip and ended up in a joint paper (together with D. Parra) submitted in January 2017. During the fall and the winter, a joint work on quantum walk was also realized with A. Suzuki (Kyushu University) and R. Tiedra de Aldecoa (Santiago de Chile). This collaboration was eased by the stay of R. Tiedra de Aldecoa in Nagoya in January/February 2017. A second paper with the same authors is in preparation. A second work with J. Derezinski is also in preparation. A short trip to France for collaborations was organized in January 2017.

Remarks

Much more information on research and teaching can be found on
http://www.math.nagoya-u.ac.jp/~richard/

  • Research Products

    (11 results)

All 2017 2016

All Journal Article (5 results) (of which Int'l Joint Research: 5 results,  Peer Reviewed: 5 results,  Open Access: 3 results,  Acknowledgement Compliant: 3 results) Presentation (6 results) (of which Invited: 6 results)

  • [Journal Article] On Schroedinger operators with inverse square potentials on the half-line2017

    • Author(s)
      J. Derezinski, S. Richard
    • Journal Title

      Ann. Henri Poincare

      Volume: 18 Pages: 869 - 928

    • DOI

      DOI 10.1007/s00023-016-0520-7

    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Spectral and scattering properties at thresholds for the Laplacian in a half-space with a periodic boundary condition2017

    • Author(s)
      S. Richard, R. Tiedra de Aldecoa
    • Journal Title

      J. Math. Anal. Appl.

      Volume: 446 Pages: 1695 - 1722

    • DOI

      http://dx.doi.org/10.1016/j.jmaa.2016.09.045

    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Low energy spectral and scattering theory for relativistic Schroedinger operators2016

    • Author(s)
      S. Richard, T. Umeda
    • Journal Title

      Hokkaido Mathematical Journal

      Volume: 45 Pages: 141 - 179

    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Resolvent expansions and continuity of the scattering matrix at embedded thresholds: the case of quantum waveguides2016

    • Author(s)
      S. Richard, R. Tiedra de Aldecoa
    • Journal Title

      Bull. Soc. math. France

      Volume: 144 Pages: 251 - 277

    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Continuity of the spectra for families of magnetic operators on Z^d,2016

    • Author(s)
      D. Parra, S. Richard
    • Journal Title

      Anal. Math. Phys.

      Volume: 6 Pages: 327 - 343

    • DOI

      DOI 10.1007/s13324-015-0121-5

    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Presentation] Spectral and scattering theory on perturbed crystal lattices2017

    • Author(s)
      S. Richard
    • Organizer
      Seminar talk
    • Place of Presentation
      WPI AIMR Sendai
    • Year and Date
      2017-02-23
    • Invited
  • [Presentation] Operateurs de Schroedinger presque homogenes2016

    • Author(s)
      S. Richard
    • Organizer
      Seminar of mathematical physics
    • Place of Presentation
      University of Orsay
    • Year and Date
      2016-09-21
    • Invited
  • [Presentation] Operateurs de Schroedinger presque homogenes2016

    • Author(s)
      S. Richard
    • Organizer
      Seminar of mathematical physics
    • Place of Presentation
      University of Grenoble, France
    • Year and Date
      2016-09-19
    • Invited
  • [Presentation] Operateurs de Schroedinger presque homogenes2016

    • Author(s)
      S. Richard
    • Organizer
      Seminar of EDP, analysis and applications
    • Place of Presentation
      University of Lorraine, France
    • Year and Date
      2016-09-16
    • Invited
  • [Presentation] Continuite du spectre pour des familles d'operateurs magnetiques sur Z^d2016

    • Author(s)
      S. Richard
    • Organizer
      Seminar of analysis, geometry and algebra
    • Place of Presentation
      University of Lorraine, France
    • Year and Date
      2016-09-15
    • Invited
  • [Presentation] Theorie spectrale et de la diffusion sur des cristaux topologiques perturbes2016

    • Author(s)
      S. Richard
    • Organizer
      Seminar of analysis
    • Place of Presentation
      University of Bordeaux, France
    • Year and Date
      2016-09-12
    • Invited

URL: 

Published: 2018-01-16  

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