Dirk Hundertmark
Associate Professor
Department of Mathematics
University of Illinois at
UrbanaChampaign
1409 W. Green Street (MC382)
Urbana, Illinois 61801
Office: Altgeld Hall 371.
Phone: (217) 3334023.
Fax: (217) 3339576.
email: dirk at math dot uiuc dot edu
Teaching:
Math 347 Fundamental Mathematics
Previous teaching
Diplom in Physics (M.Sc.), Friedrich Alexander Universität
ErlangenNürnberg (Germany), 1992
Doktor rer.nat. (Ph.D.), Ruhr Universität Bochum (Germany), 1996
Research Interests
Partial differential equations, analysis, including
functional analysis, spectral theory, variational methods, motivated by problems from
Physics, especially quantum mechanics, and Engineering.
Spectral theory of random operators and and its connection to statistical mechanics and
some probabilistic problems from solid state physics.
More recently, mathematical problems in nonlinear fiberoptics, especially properties of dispersion managed solitons.
A short cv is available here
Publications

Exponential decay of dispersion management solitons,
with Burak Erdogan and YoungRan Lee. Accepted for publication by MRL. [pdf file]
 Heatflow monotonicity of Strichartz norms,
with Jonathan Bennett, Neal Bez, and Anthony Carbery, Analysis & PDE 2 (2009), no. 2, 147–158.
[psfile or
pdffile]

Decay estimates and smoothness for solutions of
the dispersion managed nonlinear Schrödinger equation,
(with YoungRan Lee) 23 pp. Communications in Mathematical Physics, 286 (2009), no. 3, 851–873.
[.ps file
or .pdf file]

Improved HardySobolev inequalities, (with Alex Balinsky, Des Evans,
and Roger Lewis.) Banach Journal of Mathematical Analysis 2 (2008),
no. 2, 94106. [psfile or pdffile]

A short introduction to Anderson localization,
in proceedings of the LMS Meeting on Analysis and Stochastics
of Growth Processes and Interface Models, Bath, September 2006.
Oxford Univ. Press, Oxford, 2008, 194–218,.
[psfile or
pdffile]
 A unified theoretical framework for fluctuatingcharge models in atomspace and in bondspace,
with Jiahao Chen and Todd Martinez, Journal of Chemical Physics 129, 214113 (2008).

Eigenvalue bounds in the gaps of Schrödinger operators and Jacobi matrices,
(with Barry Simon),
Journal of Mathematical Analysis and its Applications, 340 (2007), no. 2, 892900.

Exponential decay of eigenfunctions and generalized eigenfunction
of non selfadjoint matrix Schrödinger operators related to NLS,
(with YoungRan Lee). Bulletin of the London Mathematical Society, 39 (2007), no. 5, 709720.16 pages
[psfile
or pdffile ]

Bound state problems in Quantum Mechanics, in
Spectral theory and mathematical physics: a Festschrift in honor of
Barry Simon's 60th birthday, 463496,
Proc. Sympos. Pure Math. 76, Part 1,
Amer. Math. Soc., Providence, RI, 2007.
[psfile or pdffile]
 On sharp Strichartz inequalites in low dimensions (with Vadim
Zharnitsky), accepted for publication in International mathematical
Research Noticees. [psfile
or pdffile]
 Bounds on the spectral shift function and the density of states
(with Rowan Killip, Shu Nakamura, Peter Stollmann, and Ivan VeseliÄ‡),
accepted for publication in Communications in Mathematical Physics.
[psfile or pdffile]
 A diamagnetic inequality for semigroup differences (with Barry
Simon), Journal
für die Reine und Angewandte Mathematik (Crelle's journal) 571 (2004), 107130. [.ps
file or .pdf
file]
 Reflection symmetries and absence of eigenvalues
for onedimensional Schrödinger operators (with David Damanik),
Proceedings of the American Mathematical Society 132
(2004), no. 7, 19571962. [.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),
651660. [.ps
file or .pdf
file]
 Bound states and the SzegÅ‘ condition for Jacobi matrices and Schrödinger operators
(with David Damanik and Barry Simon), J. Funct. Anal. 205 (2003), no. 2, 357379. [.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), 545562. [psfile
or pdffile].
 LiebThirring inequalities for Jacobi matrices
(with Barry Simon), J. Approx. Theory 118 (2002), 106130, [.ps file
or .pdf
file].
 On the number of bound states for Schrödinger
operators with operatorvalued potentials, Arkiv för matematik 40
(2002), 7387, [.ps file
or .pdf
file]
 An optimal L^{p}bound on the Krein spectral shift
function (with Barry Simon), J. d'Analyse Math. 87
(2002),199208, [.ps
file or .pdf
file].
 Finitevolume fractionalmoment criteria for Anderson
localization (with Michael Aizenman, Roland Friedrich, and Jeffrey
Schenker), Communications in Mathematical Physics 224 (1)
(2001), 219253,
[.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), 213238, [.ps file
or .pdf file]
 Constructive fractionalmoment criteria for localization in
random operators (with Michael Aizenman, Roland Friedrich, and Jeffrey
Schenker), Physica A 279 (2000), 369377.
 New bounds on the LiebThirring constant (with Ari Laptev and
Timo Weidl), Inventiones Mathematica 140 (2000), 693704.
[psfile
or pdffile ]
 A sharp bound on the instability of the relativistic
electronpositron field (with Norbert Röhrl and Heinz Siedentop),
Communications in Mathematical Physics 210 (3), (2000) 629642.
 On the timedependent approach to Anderson localization,
Mathematische Nachrichten 214 (2000), 2538.
 Continuity properties of Schrödinger semigroups with magnetic
fields (with Kurt Broderix and Hajo Leschke), Reviews in Mathematical
Physics 12 (2000), 181225
 A sharp bound for an eigenvalue moment of the onedimensional
Schrödinger operator (with Elliott H. Lieb and Lawrence E. Thomas),
Advances in Theoretical and Mathematical Physics 2 (4) (1998),
719731
 The fate of Lifshitz tails in magnetic fields (with Kurt
Broderix, Werner Kirsch, and Hajo Leschke), Journal of Statistical
Physics 80 (1995), 122
 Selfaveraging, 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)
Preprints

Superexponential decay of diffraction managed solitons, with YoungRan Lee.
[psfile or pdffile]
 On nonlocal variational problems with lack of compactness related to nonlinear optics, with YoungRan Lee.
[psfile or pdffile]

Analyticity of extremals to the AiryStrichartz inequality, with Shuanglin Shao.
[pdffile]
In preparation:
 Continuity properties of magnetic Schrödinger semigroups with
rough vector potentials.

A simple proof of analyticity of solitarywave solutions for a large class of nonlinear evolution equations, with Jeff Selden.
Transparencies from talks
 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]
Click
here to get a listing of D. Hundertmark's papers from the AMS
MathSciNet with links to Mathematical Reviews.
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Last changes: 19 January 2009.