Institut für Angewandte Mathematik (Math D)
Dr. Markus Holzmann
Postal Address Technische Universität Graz
Institut für Angewandte Mathematik
Steyrergasse 30
8010 Graz
Austria
Phone+43-(0)316-873 8124
Telefax+43-(0)316-873 8621
RoomST 03 156
Electronic Mail holzmann@math.tugraz.at
Office hour by arrangement

Teaching Summer Term 2019

Teaching Winter Term 2018/19

Topics of Interest
  • Dirac operators with δ-shell interactions
  • Self-adjoint Dirac operators on domains
  • Approximation problems for partial differential operators
  • Spectral properties of partial differential operators with singular interactions
  • Extension theory of symmetric operators

I was participating in the following projects:

Prize
  • 2018: I was awarded with the best paper award of the Doctoral School Mathematics and Scientific Computing.
Publications
Refereed publications
  1. J. Behrndt, M. Holzmann:
    On Dirac operators with electrostatic δ-shell interactions of critical strength,
    accepted for publication in J. Spectral Theory; arXiv.

  2. M. Holzmann, V. Lotoreichik:
    Spectral analysis of photonic crystals made of thin rods,
    Asymptot. Anal. 110 (1-2) (2018), 83-112; arXiv.

  3. M. Holzmann, T. Ourmieres-Bonafos, K. Pankrashkin:
    Dirac operators with Lorentz scalar shell interactions,
    Rev. Math. Phys. 30 (2018), 1850013 (46 pages); arXiv.

  4. J. Behrndt, P. Exner, M. Holzmann, V. Lotoreichik:
    On the spectral properties of Dirac operators with electrostatic δ-shell interactions,
    J. Math. Pures Appl. 111 (2018), 47-78; arXiv.

  5. J. Behrndt, P. Exner, M. Holzmann, V. Lotoreichik:
    Approximation of Schrödinger operators with δ-interactions supported on hypersurfaces,
    Math. Nachr. 290 (2017), 1215–1248; arXiv.

Submitted papers
  1. J. Behrndt, P. Exner, M. Holzmann, V. Lotoreichik:
    The Landau Hamiltonian with δ-potentials supported on curves, arXiv.

Conference proceedings
  1. J. Behrndt, P. Exner, M. Holzmann, V. Lotoreichik:
    On Dirac operators in R^3 with electrostatic and Lorentz scalar δ-shell interactions,
    accepted for publication in Quantum Stud.: Math. Found., arXiv.

  2. J. Behrndt, M. Holzmann, V. Lotoreichik:
    Convergence of 2D-Schrödinger operators with local scaled short-range interactions to a Hamiltonian with infinitely many δ-point interactions,
    Proc. Appl. Math. Mech. 14 (2014), 1005–1006.
Thesis
  1. M. Holzmann,
    Spectral Analysis of Transmission and Boundary Value Problems for Dirac Operators,
    PhD. Thesis, TU Graz, 2018.
  2. M. Holzmann,
    Approximation of Schrödinger operators with δ-interactions supported on hypersurfaces,
    Master Thesis, TU Graz, 2014, pdf.