Dirk Hundertmark
Olga Taussky-John Todd Instructor of Mathematics

Diplom in Physics (M.Sc.), Friedrich Alexander Universität Erlangen-Nürnberg (Germany), 1992
Doktor rer.nat. (Ph.D.), Ruhr Universität Bochum (Germany), 1996

Research Interests
Mathematical physics, especially Schrödinger operators. Eigenvalue moments, spectral theory.

Publications

• (with David Damanik) Reflection symmetries and absence of eigenvalues for one-dimensional Schrödinger operators, to appear in Proc. Amer. Math. Soc.   [.ps file or .pdf file]
• (with Barry Simon) Lieb-Thirring inequalities for Jacobi matrices, to appear in Journal of Approximation Theory [.ps file or .pdf file]
• On the number of bound states for Schrödinger operators with operator-valued potentials, Arkiv för matematik 40 (2002), 73–87 [.ps file or .pdf file]
• (with Barry Simon) An optimal L^pbound on the Krein spectral shift function, to appear in J. d'Analyse Math. [.ps file or .pdf file]
• (with Michael Aizenman, Roland Friedrich, and Jeffrey Schenker) Finite-volume fractional-moment criteria for Anderson localization, to appear in   Communications in Mathematical Physics 224 (1) (2001), 219–253 [.ps file or .pdf file] 
• (with Werner Kirsch) Spectral theory of sparse potentials, in Stochastic Processes, Physics and Geometry: New Interplays. A Volume in Honor of Sergio Albeverio. Canadian Mathematical Society Conference Proceedings 28 (2000), 213–238.
• On the time-dependent approach to Anderson localization, Mathematische Nachrichten 214 (2000), 25–38
• (with Michael Aizenman, Roland Friedrich, and Jeffrey Schenker) Constructive fractional-moment criteria for localization in random operators, Physica Acta 279 (2000), 369–377
• (with Ari Laptev and Timo Weidl) New bounds on the Lieb-Thirring constant, Inventiones Mathematica 140 (2000), 693–704
• (with Norbert Röhrl and Heinz Siedentop) A sharp bound on the instability of the relativistic electron-positron field, Communications in Mathematical Physics 210 (3), (2000) 629–642
• (with Kurt Broderix and Hajo Leschke) Continuity properties of Schrödinger semigroups with magnetic fields, Reviews in Mathematical Physics  12 (2000), 181–225
• (with Elliott H. Lieb and Lawrence E. Thomas) A sharp bound for an eigenvalue moment of the one-dimensional Schrödinger operator, Advances in Theoretical and Mathematical Physics 2 (4) (1998), 719–731
• (with Kurt Broderix, Werner Kirsch, and Hajo Leschke) The fate of Lifshitz tails in magnetic fields, Journal of Statistical Physics 80 (1995), 1–22
• (with Kurt Broderix and Hajo Leschke) Self-averaging, decomposition, and asymptotic properties of the density of states for random Schrödinger operators with constant magnetic field, in "Path integrals from meV to MeV", Tutzing (1993), eds. H. Grabert, A. Inomata, and U. Weiss. World Scientific, Singapore (1993)

Preprint:

• Bound states and the Szegö condition for Jacobi matrices and Schrödinger operators (with David Damanik and Barry Simon)  [.ps file or .pdf file]

In preparation:

• A second look at the Feynman-Kac-Itô formula
• A diamagnetic inequality for semigroup differences (with Barry Simon)

Transparencies from talks

• An optimal L^p bound on the Krein spectral shift function
  Click here for the .dvi file or .ps file or .pdf file
• A diamagentic inequality for semigroup differences
  Click here for the .dvi file or .ps file or .pdf file

Courses Taught

• Fall 2000–01: Ma 108a - Classical Analysis
• Winter 2000–01: Ma 108b - Classical Analysis
• Spring 2000–01:  Ma 191i - Introduction to Schrödinger Operators
• Fall 2001–02: Ma 144a - Probability
• Winter 2001–02: Ma 144b - Probability

Contact Information
E-mail: dirkh@its.caltech.edu
Phone: (626) 395-4322
Fax: (626) 585-1728
Mailing address: Mathematics 253-37, Caltech, Pasadena, CA 91125

Click here to get a listing of D. Hundertmark's papers from the AMS MathSciNet with links to Mathematical Reviews.
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