Studieren in Chemnitz. Wissen, was gut ist.






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Research Interests:

     

  • Spectral theory of random Schrödinger operators

     

  • Dirichlet forms and weak solutions

     

  • Quantum graphs

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  • Laplacians on discrete structures with negative curvature

     

  • Mathematical diffraction theory

     

  • Dynamical systems of low complexity

Research supported by DFG from 2004 - 2007 in Einzelf\"orderung (joint project with Prof. Dr. P. Stollmann)

Research supported by DFG within Schwerpunktprogramm "Quasikristalle" from 2001- 2003 (joint project with Prof. Dr. P. Stollmann).

 

Supervision of dissertational projects:

     

  • Matthias Keller. Topic: "Spectral theory of certain tilings of the plane" (funded by sdw).

    - Matthias Keller: The essential spectrum of the Laplacian on rapidly branching tessellations, (0712.3816)

     

  • Carsten Schubert. Topic in the field of quantum graphs, joint supervision with Prof. Dr. P. Stollmann.

    - Daniel Lenz, Carsten Schubert, Peter Stollmann: Eigenfunction expansion for Schrodinger operators on metric graphs, to appear in: Integral Equations and Operator Theory, (0801.1376)



  • Daniel Wingert. Topic in the field of non-local Dirichlet forms, joint supervision with Prof. Dr. P. Stollmann


  • Adnene Besbes, Universite Paris 7. Topic: "Ergodic theorems on aperiodic tilings and applications", graduated July 2008, joint supervision with Prof. Dr. A. Boutet de Monvel, Universite Paris 7.

    - Adnene Besbes, Daniel Lenz: Delone sets with finite local complexity: Linear repetitivity versus positivity of weights, in preparation.

    - Adnene Besbes: Uniformly subadditive ergodic theorems on aperiodic linearly repetitive tilings and applications, Rev. Math. Phys. 20 (2008), 597--623. old version

     

  • Steffen Klassert. Topic: "Random operators on Delone sets", graduated May 2007, joint supervision with Prof. Dr. P. Stollmann (funded by DFG).

    - Steffen Klassert, Daniel Lenz, Peter Stollmann, Absence of absolutely continuous spectrum for one-dimensional Delone dynamical systems, in preparation.

    - Steffen Klassert, Daniel Lenz, Norbert Peyerimhoff, Peter Stollmann: Elliptic operators on planar graphs: Unique continuation for eigenfunctions and nonpositive curvature, Proceedings of the American Mathematical Society, 134, (2006) 1549--1559. (math-ph/0410022)

    - Steffen Klassert, Daniel Lenz, Peter Stollmann: Discontinuities of the integrated density of states for random operators on Delone sets, Commun. Math. Phys. 241 (2003), 235--243. (math-ph/0208027)
 
 

Supervision of Diploma theses:

     

  • Carsten Schubert, "Laplace-Operatoren auf Quantengraphen", Diplom December 2006, (joint supervision with Prof. Dr. P. Stollmann).

     

  • Matthias Keller, "Produkte zuf\"alliger Matrizen und der Lyapunov-Exponent", Diplom June 2006, (joint supervision with Prof. Dr. P. Stollmann).