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 2020

Teaching Winter Term 2019/20

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:
  • OEAD Scientific Cooperation Austria - Czech Republic
    Dirac and magnetic Schrödinger operators with singular interactions (2017/18)
  • OEAD Scientific Cooperation Austria - France
    Spectral analysis of boundary value problems (2017/18)

Prize
  • 2018: I was awarded with the best paper award of the Doctoral School Mathematics and Scientific Computing.
Publications
Refereed publications
  1. M. Holzmann, G. Unger:
    Boundary integral formulations of eigenvalue problems for elliptic differential operators with singular interactions and their numerical approximation by boundary element methods,
    accepted for publication in Oper. Matrices (2020); arXiv.

  2. J. Behrndt, M. Holzmann, T. Ourmieres-Bonafos, K. Pankrashkin:
    Two-dimensional Dirac operators with singular interactions supported on closed curves,
    J. Funct. Anal. 279 (8) (2020), 108700 (47 pages); arXiv.

  3. J. Behrndt, M. Holzmann, A. Mas:
    Self-adjoint Dirac operators on domains in R^3,
    Ann. Henri Poincare 21 (2020), 2681-2735; arXiv.

  4. J. Behrndt, M. Holzmann, A. Mantile, A. Posilicano:
    Limiting absorption principle and scattering matrix for Dirac operators with δ-shell interactions,
    J. Math. Phys. 61 (2020), 033504 (16 pages); arXiv.

  5. J. Behrndt, P. Exner, M. Holzmann, V. Lotoreichik:
    The Landau Hamiltonian with δ-potentials supported on curves,
    Rev. Math. Phys. 32 (4) (2020), 2050010 (51 pages); arXiv.

  6. J. Behrndt, M. Holzmann:
    On Dirac operators with electrostatic δ-shell interactions of critical strength,
    J. Spectral Theory 10 (1) (2020), 147-184; arXiv.

  7. J. Behrndt, P. Exner, M. Holzmann, V. Lotoreichik:
    On Dirac operators in R^3 with electrostatic and Lorentz scalar δ-shell interactions,
    Quantum Stud.: Math. Found. 6 (3) (2019), 295-314; arXiv.

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

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

  10. 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.

  11. 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. M. Holzmann:
    A note on the three dimensional Dirac operator with zigzag type boundary conditions, arXiv.

Other publications
  1. M. Holzmann:
    The nonrelativistic limit of Dirac operators with Lorentz scalar δ-shell interactions,
    Proc. Appl. Math. Mech. 19 (2019), e201900126 (2 pages).

  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.