Dirk Hundertmark

Office: Altgeld Hall 371.
Phone: (217) 333-4023.
Fax: (217) 333-9576.
e-mail: dirk at math dot uiuc dot edu

Teaching: Differential Equations, section C1
Previous teaching

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

Research Interests
Analysis, variational methods, and PDEs. Mathematical physics, especially Schrödinger operators and probability. Eigenvalue moments, spectral theory.

Publications

• Decay estimates and smoothness for solutions of the dispersion managed non-linear Schrödinger equation, (with Young-Ran Lee) 23 pp. Communications in Mathematical Physics, DOI 10.1007/s00220-008-0612-4. [.ps file or .pdf file]
  
• Improved Hardy-Sobolev inequalities, (with Alex Balinsky, Des Evans, and Roger Lewis.) Banach Journal of Mathematical Analysis 2 (2008), no. 2, 94--106. [ps-file or pdf-file]
• A short introduction to Anderson localization, to appear in the proceedings of the LMS Meeting on Analysis and Stochastics of Growth Processes, Bath, September 2006, 25 pp. [ps-file or pdf-file]
  
• Eigenvalue bounds in the gaps of Schrödinger operators and Jacobi matrices, (with Barry Simon), accepted for publication by Journal of Mathematical Analysis and its Applications, 340 (2007), no. 2, 892--900.
  
• Exponential decay of eigenfunctions and generalized eigenfunction of non self-adjoint matrix Schrödinger operators related to NLS, (with Young-Ran Lee). Bulletin of the London Mathematical Society, 39 (2007), no. 5, 709--720.16 pages [ps-file or pdf-file ]
  
• Bound state problems in Quantum Mechanics, in Spectral theory and mathematical physics: a Festschrift in honor of Barry Simon's 60th birthday, 463--496, Proc. Sympos. Pure Math. 76, Part 1, Amer. Math. Soc., Providence, RI, 2007. [ps-file or pdf-file]
  
• On sharp Strichartz inequalites in low dimensions (with Vadim Zharnitsky), accepted for publication in International mathematical Research Noticees.  [ps-file or pdf-file]
  
• Bounds on the spectral shift function and the density of states (with Rowan Killip, Shu Nakamura, Peter Stollmann, and Ivan Veselić), accepted for publication in Communications in Mathematical Physics. [ps-file or pdf-file]
  
• A diamagnetic inequality for semigroup differences (with Barry Simon), Journal für die Reine und Angewandte Mathematik (Crelle's journal) 571 (2004), 107--130. [.ps file or .pdf file]
• Reflection symmetries and absence of eigenvalues for one-dimensional Schrödinger operators (with David Damanik), Proceedings of the American Mathematical Society 132 (2004), no. 7,  1957--1962.  [.ps file ].
• Classical magnetic Lifshits tails in three space dimensions: impurity potentials with slow anisotropic decay (with Werner Kirsch and Simone Warzel), Markov Processes and Related Fields 9 (2003), 651-660. [.ps file or .pdf file]
• Bound states and the Szegő condition for Jacobi matrices and Schrödinger operators (with David Damanik and Barry Simon), J. Funct. Anal. 205 (2003), no. 2, 357-379. [.ps file or .pdf file].
• Variational estimates for discrete Schrödinger operators with potentials of indefinite sign (with David Damanik, Rowan Killip, and Barry Simon), Commun. Math. Phys. 238 (2003), 545-562.  [ps-file or pdf-file].
• Lieb-Thirring inequalities for Jacobi matrices (with Barry Simon), J. Approx. Theory 118 (2002), 106-130, [.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]
• An optimal L^pbound on the Krein spectral shift function (with Barry Simon), J. d'Analyse Math. 87 (2002),199-208, [.ps file or .pdf file].
• Finite-volume fractional-moment criteria for Anderson localization (with Michael Aizenman, Roland Friedrich, and Jeffrey Schenker), Communications in Mathematical Physics 224 (1) (2001), 219-253, [.ps file or .pdf file].
• Spectral theory of sparse potentials (with Werner Kirsch), in Stochastic Processes, Physics and Geometry: New Interplays. A Volume in Honor of Sergio Albeverio. Canadian Mathematical Society Conference Proceedings 28 (2000), 213-238, [.ps file or .pdf file]
  
• Constructive fractional-moment criteria for localization in random operators (with Michael Aizenman, Roland Friedrich, and Jeffrey Schenker), Physica A 279 (2000), 369-377.
• New bounds on the Lieb-Thirring constant (with Ari Laptev and Timo Weidl), Inventiones Mathematica 140 (2000), 693-704. [ps-file or pdf-file ]
  
• A sharp bound on the instability of the relativistic electron-positron field (with Norbert Röhrl and Heinz Siedentop), Communications in Mathematical Physics 210 (3), (2000) 629-642.
• On the time-dependent approach to Anderson localization, Mathematische Nachrichten 214 (2000), 25-38. 
• Continuity properties of Schrödinger semigroups with magnetic fields (with Kurt Broderix and Hajo Leschke), Reviews in Mathematical Physics 12 (2000), 181-225
• A sharp bound for an eigenvalue moment of the one-dimensional Schrödinger operator (with Elliott H. Lieb and Lawrence E. Thomas), Advances in Theoretical and Mathematical Physics 2 (4) (1998), 719-731
• The fate of Lifshitz tails in magnetic fields (with Kurt Broderix, Werner Kirsch, and Hajo Leschke), Journal of Statistical Physics 80 (1995), 1-22
• Self-averaging, decomposition, and asymptotic properties of the density of states for random Schrödinger operators with constant magnetic field (with Kurt Broderix and Hajo Leschke), in "Path integrals from meV to MeV", Tutzing (1993), eds. H. Grabert, A. Inomata, and U. Weiss. World Scientific, Singapore (1993)

• A unified theoretical framework for fluctuating-charge models in atom-space and in bond-space, with Jiahao Chen and Todd Martinez, 44pp.
  
• Heat-flow monotonicity of Strichartz norms, with Jonathan Bennett, Neal Bez, and Anthony Carbery, 11 pp. [ps-file or pdf-file]
  
• Super-exponential decay of diffraction managed solitons, with Young-Ran Lee. [ps-file or pdf-file]
  

• Continuity properties of magnetic Schrödinger semigroups with rough vector potentials.
  
• On the existence of dispersion management solitons for vanishing residual dispersion, with Young-Ran Lee.
  
• Exponential decay of dispersion management solitons, with Burak Erdogan and Young-Ran Lee. [draft]
  

• An optimal L^p bound on the Krein spectral shift function. [.ps file or .pdf file]
• A diamagnetic inequality for semigroup differences. [.ps file or pdf file]
• Variational estimates for discrete Schrödinger operators with potentials of indefinite sign. [.ps file or .pdf file]
• On sharp Strichartz inequalities in low dimensions. [.ps file or .pdf file]
• Decay estimates for Dispersion Management Solitons. [.ps file or .pdf file]

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