David Damanik
Associate Professor of Mathematics

Contact Information
Office: Room 434, Herman Brown Hall
Phone: (713) 348-3273
Fax: (713) 348-5231
E-mail: [my last name] at rice dot edu
Mailing address: Department of Mathematics, MS-136, Rice University, Houston, TX 77251

Degrees
Dr. phil. nat., Johann Wolfgang Goethe-Universität, Frankfurt, Germany, 1998
Dipl.-Inform., Johann Wolfgang Goethe-Universität, Frankfurt, Germany, 1996
Dipl.-Math., Johann Wolfgang Goethe-Universität, Frankfurt, Germany, 1995

Research Interests
Schrödinger operators, quasicrystal models, consequences of complexity and disorder in spectral theory

Publications (Click here for a list of coauthors)

• Absolute continuity of the integrated density of states for the almost Mathieu operator with non-critical coupling (with Artur Avila), Invent. Math. 172 (2008), 439-453
• The fractal dimension of the spectrum of the Fibonacci Hamiltonian (with Mark Embree, Anton Gorodetski, and Serguei Tcheremchantsev), Commun. Math. Phys. 280 (2008), 499-516
• The analytic theory of matrix orthogonal polynomials (with Alexander Pushnitski and Barry Simon), Surv. Approx. Theory 4 (2008), 1-85
• Lyapunov exponents of continuous Schrödinger cocycles over irrational rotations (with Kristian Bjerklöv and Russell Johnson), Ann. Mat. Pura Appl. 187 (2008), 1-6
• Upper bounds in quantum dynamics (with Serguei Tcheremchantsev), J. Amer. Math. Soc. 20 (2007), 799-827
• Schrödinger operators with many bound states (with Christian Remling), Duke Math. J. 136 (2007), 51-80
• Unbounded Jacobi matrices at critical coupling (with Sergey Naboko), J. Approx. Theory 145 (2007), 221-236
• Uniform Szegö cocycles over strictly ergodic subshifts (with Daniel Lenz), J. Approx. Theory  144 (2007), 133-138
• Bound states of discrete Schrödinger operators with super-critical inverse square potentials (with Gerald Teschl), Proc. Amer. Math. Soc. 135 (2007), 1123-1127
• Lyapunov exponents and spectral analysis of ergodic Schrödinger operators: A survey of Kotani theory and its applications, Spectral theory and mathematical physics: a Festschrift in honor of Barry Simon's 60th birthday, 539--563, Proc. Sympos. Pure Math., 76, Part 2, Amer. Math. Soc., Providence, RI, 2007
• Strictly ergodic subshifts and associated operators, Spectral theory and mathematical physics: a Festschrift in honor of Barry Simon's 60th birthday, 505--538, Proc. Sympos. Pure Math., 76, Part 2, Amer. Math. Soc., Providence, RI, 2007
• Jost functions and Jost solutions for Jacobi matrices, II. Decay and analyticity (with Barry Simon), Int. Math. Res. Not. (2006), Article ID 19396, 1-32
• Jost functions and Jost solutions for Jacobi matrices, I. A necessary and sufficient condition for Szegö asymptotics (with Barry Simon), Invent. Math. 165 (2006), 1-50
• Lower transport bounds for one-dimensional continuum Schrödinger operators  (with Daniel Lenz and Günter Stolz), Math. Ann. 336 (2006), 361-389
• Verblunsky coefficients with Coulomb-type decay, J. Approx. Theory, 139 (2006), 257-268  
• Zero-measure Cantor spectrum for Schrödinger operators with low-complexity potentials (with Daniel Lenz), J. Math. Pures Appl. 85 (2006), 671-686
• A criterion of Boshernitzan and uniform convergence in the multiplicative ergodic theorem (with Daniel Lenz), Duke Math. J. 133 (2006), 95-123
• Substitution dynamical systems: characterization of linear repetitivity and applications (with Daniel Lenz), J. Math. Anal. Appl. 321 (2006), 766-780
• Generic singular spectrum for ergodic Schrödinger operators (with Artur Avila), Duke Math. J. 130 (2005), 393-400
• Scaling estimates for solutions and dynamical lower bounds on wavepacket spreading (with Serguei Tcheremchantsev), J. d'Analyse Math. 97 (2005), 103-131
• Schrödinger operators with few bound states (with Rowan Killip and Barry Simon),  Commun. Math. Phys. 258 (2005), 741-750
• Almost everywhere positivity of the Lyapunov exponent for the doubling map (with Rowan Killip), Commun. Math. Phys. 257 (2005), 287-290
• Ergodic potentials with a discontinuous sampling function are non-deterministic (with Rowan Killip), Math. Res. Lett. 12 (2005), 187-192
• Dynamical upper bounds for one-dimensional quasicrystals, J. Math. Anal. Appl. 303 (2005), 327-341
• Half-line Schrödinger operators with no bound states (with Rowan Killip),  Acta Math. 193 (2004), 31-72
• Power-law bounds on transfer matrices and quantum dynamics in one dimension, II (with András Sütö and Serguei Tcheremchantsev), J. Funct. Anal. 216 (2004), 362-387
• Necessary and sufficient conditions in the spectral theory of Jacobi matrices and Schrödinger operators (with Rowan Killip and Barry Simon), Int. Math. Res. Not. (2004), no. 22, 1087-1097
• Localization for discrete one-dimensional random word models (with Robert Sims and Günter Stolz), J. Funct. Anal. 208 (2004), 423-445
• A version of Gordon's theorem for multi-dimensional Schrödinger operators, Trans. Amer. Math. Soc. 356 (2004), 495-507
• Half-line eigenfunction estimates and singular continuous spectrum of zero Lebesgue measure (with Daniel Lenz), Forum Math. 16 (2004), 109-128
• Reflection symmetries and absence of eigenvalues for one-dimensional Schrödinger operators (with Dirk Hundertmark), Proc. Amer. Math. Soc. 132 (2004), 1957-1962
• Palindrome complexity (with Jean-Paul Allouche, Michael Baake and Julien Cassaigne), Theoret. Comput. Sci. 292 (2003), 9-31
• Powers in Sturmian sequences (with Daniel Lenz), European J. Combin. 24 (2003), 377-390
• Log-dimensional spectral properties of one-dimensional quasicrystals (with Michael Landrigan), Proc. Amer. Math. Soc. 131 (2003), 2209-2216
• Power-law bounds on transfer matrices and quantum dynamics in one dimension (with Serguei Tcheremchantsev), Commun. Math. Phys. 236 (2003), 513-534
• Variational estimates for discrete Schrödinger operators with potentials of indefinite sign (with Dirk Hundertmark, Rowan Killip, and Barry Simon), Commun. Math. Phys. 238 (2003), 545-562
• Uniform spectral properties of one-dimensional quasicrystals, IV. Quasi-Sturmian potentials (with Daniel Lenz), J. d'Analyse Math. 90 (2003), 115-139
• Quantum dynamical bounds for one-dimensional quasicrystals, Contemp. Math. 327 (2003), 87-97
• Combinatorial properties of Arnoux-Rauzy subshifts and applications to Schrödinger operators (with Luca Q. Zamboni), Rev. Math. Phys. 15 (2003), 745-763
• Bound states and the Szegö condition for Jacobi matrices and Schrödinger operators (with Dirk Hundertmark and Barry Simon),  J. Funct. Anal. 205 (2003), 357-379
• The index of Sturmian sequences (with Daniel Lenz), European J. Combin. 23 (2002), 23-29
• Some high-complexity Hamiltonians with purely singular continuous spectrum (with Boris Solomyak),  Ann. Henri Poincare 3 (2002), 99-105
• Lyapunov exponents in continuum Bernoulli-Anderson models (with Robert Sims and Günter Stolz), Operator Theory: Advances and Applications 132, Birkhäuser, Basel (2002), pp. 121-130
• Localization for one-dimensional, continuum, Bernoulli-Anderson models (with Robert Sims and Günter Stolz), Duke Math. J. 114 (2002), 59-100
• Absence of eigenvalues for a class of Schrödinger operators on the strip, Forum Math. 14 (2002), 797-806.
• Linearly recurrent circle map subshifts and an application to Schrödinger operators (with Boris Adamczewski), Ann. Henri Poincare 3 (2002), 1019-1047
• Multi-scale analysis implies strong dynamical localization (with Peter Stollmann), Geom. Funct. Anal. 11 (2001), 11-29
• Uniform singular continuous spectrum for the period doubling Hamiltonian, Ann. Henri Poincare 2 (2001), 101-108
• Spectral theory of Schrödinger operators with low-complexity potentials, Ferroelectrics 250 (2001), 143-149
• Linear repetitivity, I. Uniform subadditive ergodic theorems and applications (with Daniel Lenz), Discrete Comput. Geom. 26 (2001), 411-428
• A palindromic half-line criterion for absence of eigenvalues and applications to substitution Hamiltonians (with Jean-Michel Ghez and Laurent Raymond), Ann. Henri Poincare 2 (2001), 927-939
• Local symmetries in the period doubling sequence, Discrete Appl. Math. 100 (2000), 115-121
• A generalization of Gordon's theorem and applications to quasiperiodic Schrödinger operators (with Günter Stolz), Electron. J. Diff. Eqns. 2000 (2000), No. 55, pp. 1-8
• Palindrome complexity bounds for primitive substitution sequences (with Douglas Zare), Discrete Math. 222 (2000), 259-267
• Substitution Hamiltonians with bounded trace map orbits, J. Math. Anal. Appl. 249 (2000), 393-411
• Gordon-type arguments in the spectral theory of one-dimensional quasicrystals, in Directions in Mathematical Quasicrystals, M. Baake, R. V. Moody, eds., CRM Monograph Series 13, AMS, Providence, RI (2000), pp. 277-304
• Reflection symmetries of almost periodic functions (with Rowan Killip), J. Funct. Anal. 178 (2000), 251-257
• Singular continuous spectrum for a class of substitution Hamiltonians II., Lett. Math. Phys. 54 (2000), 25-31
• Uniform spectral properties of one-dimensional quasicrystals, III. alpha-continuity (with Rowan Killip and Daniel Lenz), Commun. Math. Phys. 212 (2000), 191-204
• Uniform spectral properties of one-dimensional quasicrystals, II. The Lyapunov exponent (with Daniel Lenz), Lett. Math. Phys. 50 (1999), 245-257
• Uniform spectral properties of one-dimensional quasicrystals, I. Absence of eigenvalues (with Daniel Lenz), Commun. Math. Phys. 207 (1999), 687-696
• Singular continuous spectrum for a class of substitution Hamiltonians, Lett. Math. Phys. 46 (1998), 303-311
• Singular continuous spectrum for the period doubling Hamiltonian on a set of full measure, Commun. Math. Phys. 196 (1998), 477-483
• alpha-continuity properties of one-dimensional quasicrystals, Commun. Math. Phys. 192 (1998), 169-182

Preprints 

• Cantor spectrum for Schrödinger operators with potentials arising from generalized skew-shifts (with Artur Avila and Jairo Bochi),  to appear in Duke Math. J.    arXiv:0709.2667
• Generic continuous spectrum for ergodic Schrödinger operators (with Michael Boshernitzan),  to appear in Commun. Math. Phys.    arXiv:0708.1263

Teaching 

• MATH 423: Partial Differential Equations (Fall 2007)  course webpage
• MATH 521: Advanced Topics in Real Analysis (Fall 2007)  course webpage
• MATH 699: VIGRE Seminar (Fall 2007)  seminar webpage
• MATH 102: Single Variable Calculus II (Fall 2006)  course webpage
• MATH 423: Partial Differential Equations (Fall 2006)  course webpage

Further Items 

• Geometry-Analysis Seminar  list of talks
• Jones College  college webpage