David Damanik
Robert L. Moody, Sr. Professor
Department Chair
Contact Information
Office: Room
434, Herman Brown Hall
Phone: (713) 3483273
Fax: (713)
3485231
Email: [my last name] at rice dot edu
Mailing address: Department of Mathematics, MS136, Rice University, Houston, TX 77251
Degrees
Dr. phil. nat., Johann Wolfgang GoetheUniversität, Frankfurt, Germany, 1998
Dipl.Inform., Johann Wolfgang GoetheUniversität, Frankfurt, Germany, 1996
Dipl.Math., Johann Wolfgang GoetheUniversität, Frankfurt, Germany, 1995
Research Interests
Spectral Theory, Dynamical Systems, Aperiodic Order
Publications

The isospectral torus of quasiperiodic Schrödinger operators via periodic approximations (with Michael Goldstein and Milivoje Lukic), Invent. Math. 207 (2017), 895980

A multiscale analysis scheme on Abelian groups with an application to operators dual to Hill's equation (with Michael Goldstein and Milivoje Lukic), Trans. Amer. Math. Soc. 369 (2017), 16891755

On the existence and uniqueness of global solutions for the KdV equation with quasiperiodic initial data (with Michael Goldstein), J. Amer. Math. Soc. 29 (2016), 825856

The Fibonacci Hamiltonian (with Anton Gorodetski and William Yessen), Invent. Math. 206 (2016), 629692

An extension of the KunzSouillard approach to localization in one dimension and applications to almostperiodic Schrödinger operators (with Anton Gorodetski), Adv. Math. 297 (2016), 149173

Counterexamples to the KotaniLast conjecture for continuum Schrödinger operators via characterautomorphic Hardy spaces (with Peter Yuditskii), Adv. Math. 293 (2016), 738781

Spreading estimates for quantum walks on the integer lattice via powerlaw bounds on transfer matrices (with Jake Fillman and Darren Ong), J. Math. Pures Appl. 105 (2016), 293341

On anomalous LiebRobinson bounds for the Fibonacci XY chain (with Marius Lemm, Milivoje Lukic and William Yessen), J. Spectr. Theory 6 (2016), 601628

The spectrum of a Schrödinger operator with small quasiperiodic potential is homogeneous (with Michael Goldstein and Milivoje Lukic), J. Spectr. Theory 6 (2016), 415427

Quantum intermittency for sparse CMV matrices with an application to quantum walks on the halfline (with Jon Erickson, Jake Fillman, Gerhardt Hinkle, Alan Vu), J. Approx. Theory 208 (2016), 5984

What is ... aperiodic order? (with Michael Baake and Uwe Grimm), Notices Amer. Math. Soc. 63 (2016), 647650

Characterizations of uniform hyperbolicity and spectra of CMV matrices (with Jake Fillman, Milivoje Lukic, and William Yessen), Discrete Contin. Dyn. Syst. S 9 (2016), 10091023

Open problems and conjectures related to the theory of mathematical quasicrystals (with Faustin Adiceam, Franz Gähler, Uwe Grimm, Alan Haynes, Antoine Julien, Andrés Navas, Lorenzo Sadun and Barak Weiss), Arnold Math. J. 2 (2016), 579592

Absolutely continuous convolutions of singular measures and an application to the square Fibonacci Hamiltonian (with Anton Gorodetski and Boris Solomyak), Duke Math. J. 164 (2015), 16031640

Quantum dynamics of periodic and limitperiodic Jacobi and block Jacobi matrices with applications to some quantum many body problems (with Milivoje Lukic and William Yessen), Commun. Math. Phys. 337 (2015), 15351561

Almost sure frequency independence of the dimension of the spectrum of Sturmian Hamiltonians (with Anton Gorodetski), Commun. Math. Phys. 337 (2015), 12411253

Uniform hyperbolicity for Szego cocycles and applications to random CMV matrices and the Ising model (with Jake Fillman, Milivoje Lukic, and William Yessen), Int. Math. Res. Not. 2015 (2015), 71107129

Almost ballistic transport for the weakly coupled Fibonacci Hamiltonian (with Anton Gorodetski), Israel J. Math. 206 (2015), 109126

Transport exponents of Sturmian Hamiltonians (with Anton Gorodetski, Qinghui Liu, and Yanhui Qu), J. Funct. Anal. 269 (2015), 14041440

Spectral properties of Schrödinger operators arising in the study of quasicrystals (with Anton Gorodetski and Mark Embree), Mathematics of Aperiodic Order, Birkhäuser/Springer (2015), 307370

On the inverse spectral problem for the quasiperiodic Schrödinger equation (with Michael Goldstein), Publ. Math. Inst. Hautes Études Sci. 119 (2014), 217401

Singular density of states measure for subshift and quasiperiodic Schrödinger operators (with Artur Avila and Zhenghe Zhang), Commun. Math. Phys. 330 (2014), 469498

New anomalous LiebRobinson bounds in quasiperiodic XY chains (with Marius Lemm, Milivoje Lukic and William Yessen), Phys. Rev. Lett. 113 (2014), 127202

Dynamics of unitary operators (with Jake Fillman and Robert Vance), J. Fractal Geom. 1 (2014), 391425

Continuum Schrödinger operators associated with aperiodic subshifts (with Jake Fillman and Anton Gorodetski), Ann. Henri Poincaré 15 (2014), 11231144 (This paper was awarded the 2014 Annales Henri Poincaré Prize.)

Hölder continuity of the integrated density of states for the Fibonacci Hamiltonian (with Anton Gorodetski), Commun. Math. Phys. 323 (2013), 497515

Limitperiodic Schrödinger operators on Z^d: Uniform localization (with Zheng Gan), J. Funct. Anal. 265 (2013), 435448

Orthogonal polynomials on the unit circle with Fibonacci Verblunsky coefficients, I. The essential support of the measure (with Paul Munger and William Yessen), J. Approx. Theory 173 (2013), 5688

Orthogonal polynomials on the unit circle with Fibonacci Verblunsky coefficients, II. Applications (with Paul Munger and William Yessen), J. Stat. Phys. 153 (2013), 339362

Opening gaps in the spectrum of strictly ergodic Schrödinger operators (with Artur Avila and Jairo Bochi), J. Eur. Math. Soc. 14 (2012), 61106

The density of states measure of the weakly coupled Fibonacci Hamiltonian (with Anton Gorodetski), Geom. Funct. Anal. 22 (2012), 976989

Spectral and quantum dynamical properties of the weakly coupled Fibonacci Hamiltonian (with Anton Gorodetski), Commun. Math. Phys. 305 (2011), 221277

A continuum version of the KunzSouillard approach to localization in one dimension (with Günter Stolz), J. Reine Angew. Math. 660 (2011), 99130

Limitperiodic Schrödinger operators with uniformly localized eigenfunctions (with Zheng Gan), J. d'Analyse Math. 115 (2011), 3349

Spectral properties of limitperiodic Schrödinger operators (with Zheng Gan), Commun. Pure Appl. Anal. 10 (2011), 859871

Perturbations of orthogonal polynomials with periodic recursion coefficients (with Rowan Killip and Barry Simon), Ann. of Math. 171 (2010), 19312010

Limitperiodic Schrödinger operators in the regime of positive Lyapunov exponents (with Zheng Gan), J. Funct. Anal. 258 (2010), 40104025

A general description of quantum dynamical spreading over an orthonormal basis and applications to Schrödinger operators (with Serguei Tcheremchantsev), Discrete Contin. Dyn. Syst. A 28 (2010), 13811412

Cantor spectrum for Schrödinger operators with potentials arising from generalized skewshifts (with Artur Avila and Jairo Bochi), Duke Math. J. 146 (2009), 253280

The repetition property for sequences on tori generated by polynomials or skewshifts (with Michael Boshernitzan), Israel J. Math. 174 (2009), 189202

Schrödinger operators defined by interval exchange transformations (with Jon Chaika and Helge Krüger), J. Mod. Dyn. 3 (2009), 253270

Almost periodic Szegö cocycles with uniformly positive Lyapunov exponents (with Helge Krüger), J. Approx. Theory 161 (2009), 813818

Hyperbolicity of the trace map for the weakly coupled Fibonacci Hamiltonian (with Anton Gorodetski), Nonlinearity 22 (2009), 123143

Quantum dynamical applications of Salem's theorem (with Rafael del Rio), Lett. Math. Phys. 22 (2009), 1319

The spectrum of the weakly coupled Fibonacci Hamiltonian (with Anton Gorodetski), Electron. Res. Announc. Math. Sci. 16 (2009), 2329

Almost everything about the Fibonacci operator, New Trends in Mathematical Physics, Selected contributions of the XVth International Congress on Mathematical Physics, Springer (2009), 149159

Pinned repetitions in symbolic flows: preliminary results (with Michael Boshernitzan), Discrete Contin. Dyn. Syst. 2009, Dynamical Systems, Differential Equations and Applications. 7th AIMS Conference, suppl. (2009), 869878

Absolute continuity of the integrated density of states for the almost Mathieu operator with noncritical coupling (with Artur Avila), Invent. Math. 172 (2008), 439453

Generic continuous spectrum for ergodic Schrödinger
operators (with Michael Boshernitzan), Commun. Math. Phys. 283 (2008), 647662

The fractal dimension of the spectrum of the Fibonacci Hamiltonian (with Mark Embree, Anton Gorodetski, and Serguei Tcheremchantsev), Commun. Math. Phys. 280 (2008), 499516
 The analytic theory of matrix orthogonal polynomials (with Alexander Pushnitski and Barry Simon), Surv. Approx. Theory 4 (2008), 185

Quantum dynamics via complex analysis methods: general upper bounds without timeaveraging and tight lower bounds for the strongly coupled Fibonacci Hamiltonian (with Serguei Tcheremchantsev), J. Funct. Anal. 255 (2008), 28722887
 Lyapunov exponents of continuous Schrödinger cocycles over irrational
rotations (with Kristian Bjerklöv and Russell Johnson), Ann. Mat. Pura Appl. 187 (2008), 16
 Upper bounds in quantum dynamics (with Serguei Tcheremchantsev), J. Amer. Math. Soc. 20 (2007), 799827
 Schrödinger operators with many bound states (with Christian Remling), Duke Math. J. 136 (2007), 5180

Unbounded Jacobi matrices at critical coupling (with Sergey Naboko),
J. Approx. Theory 145 (2007), 221236

Uniform Szegö cocycles over strictly ergodic subshifts (with Daniel Lenz), J. Approx. Theory
144 (2007), 133138

Bound states of discrete Schrödinger operators with supercritical inverse
square potentials (with Gerald Teschl), Proc. Amer. Math. Soc. 135 (2007), 11231127
 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, 539563, 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, 505538, 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, 132
 Jost functions and Jost solutions for Jacobi matrices, I. A necessary
and sufficient condition for Szegö asymptotics (with Barry Simon), Invent. Math. 165 (2006), 150
 Lower transport bounds for onedimensional continuum Schrödinger
operators (with Daniel Lenz and Günter Stolz), Math.
Ann. 336 (2006), 361389
 Verblunsky coefficients with Coulombtype decay, J.
Approx. Theory, 139 (2006), 257268
 Zeromeasure Cantor spectrum for Schrödinger operators with
lowcomplexity potentials (with Daniel Lenz), J. Math. Pures
Appl. 85 (2006), 671686
 A criterion of Boshernitzan and uniform convergence in the
multiplicative ergodic theorem (with Daniel Lenz), Duke
Math. J. 133 (2006), 95123
 Substitution dynamical systems: characterization of linear
repetitivity and applications (with Daniel Lenz), J.
Math. Anal. Appl. 321 (2006), 766780
 Generic singular spectrum for ergodic Schrödinger operators (with Artur
Avila), Duke Math. J. 130 (2005), 393400
 Scaling estimates for solutions and dynamical lower bounds on wavepacket
spreading (with Serguei Tcheremchantsev), J. d'Analyse Math. 97
(2005), 103131
 Schrödinger operators with few bound states (with Rowan Killip and Barry
Simon), Commun. Math. Phys. 258 (2005), 741750
 Almost everywhere positivity of the Lyapunov exponent for the doubling
map (with Rowan Killip), Commun. Math. Phys. 257
(2005), 287290
 Ergodic potentials with a discontinuous sampling function are
nondeterministic (with Rowan Killip), Math. Res. Lett. 12
(2005), 187192
 Dynamical upper bounds for onedimensional quasicrystals,
J. Math. Anal. Appl. 303 (2005), 327341
 Halfline Schrödinger operators with no bound states (with Rowan Killip),
Acta Math. 193 (2004), 3172
 Powerlaw bounds on transfer matrices and quantum dynamics in one
dimension, II (with András Sütö and Serguei Tcheremchantsev), J. Funct. Anal.
216 (2004), 362387
 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, 10871097
 Localization for discrete onedimensional random word models (with Robert
Sims and Günter Stolz), J. Funct. Anal. 208 (2004), 423445
 A version of Gordon's theorem for multidimensional Schrödinger operators, Trans. Amer. Math. Soc.
356 (2004), 495507
 Halfline eigenfunction estimates and singular continuous spectrum of zero Lebesgue
measure (with Daniel Lenz), Forum Math. 16 (2004), 109128
 Reflection symmetries and absence of eigenvalues for onedimensional
Schrödinger operators (with Dirk Hundertmark), Proc. Amer. Math. Soc. 132 (2004), 19571962
 Palindrome complexity (with JeanPaul Allouche, Michael Baake and Julien Cassaigne), Theoret. Comput. Sci.
292 (2003), 931
 Powers in Sturmian sequences (with Daniel Lenz), European
J. Combin. 24 (2003), 377390
 Logdimensional spectral properties of onedimensional quasicrystals (with Michael
Landrigan), Proc. Amer. Math. Soc.
131 (2003), 22092216
 Powerlaw bounds on transfer matrices and quantum dynamics in one
dimension (with Serguei Tcheremchantsev), Commun.
Math. Phys. 236 (2003), 513534
 Variational estimates for discrete Schrödinger operators with potentials of indefinite
sign (with Dirk Hundertmark, Rowan Killip, and Barry Simon), Commun. Math. Phys.
238 (2003), 545562
 Uniform spectral properties of onedimensional quasicrystals, IV. QuasiSturmian
potentials (with Daniel Lenz), J. d'Analyse Math.
90 (2003), 115139
 Quantum dynamical bounds for onedimensional quasicrystals, Contemp. Math. 327 (2003), 8797
 Combinatorial properties of ArnouxRauzy subshifts
and applications to Schrödinger operators (with Luca Q. Zamboni), Rev. Math. Phys. 15 (2003), 745763
 Bound states and the Szegö condition for Jacobi matrices and
Schrödinger operators (with Dirk Hundertmark and Barry Simon), J. Funct. Anal.
205 (2003), 357379
 The index of Sturmian sequences (with Daniel Lenz), European J. Combin. 23 (2002), 2329
 Some highcomplexity Hamiltonians with purely singular continuous spectrum (with Boris
Solomyak), Ann. Henri Poincare 3 (2002), 99105
 Lyapunov exponents in continuum BernoulliAnderson models (with Robert
Sims and Günter Stolz), Operator Theory: Advances and Applications 132,
Birkhäuser, Basel (2002), pp. 121130
 Localization for onedimensional, continuum, BernoulliAnderson models (with Robert Sims
and Günter Stolz), Duke Math. J. 114 (2002),
59100
 Absence of eigenvalues for a class of Schrödinger operators on the
strip, Forum Math. 14 (2002), 797806.
 Linearly recurrent circle map subshifts and an application to
Schrödinger operators (with Boris Adamczewski), Ann. Henri Poincare 3
(2002), 10191047
 Multiscale analysis implies strong dynamical localization (with Peter Stollmann), Geom.
Funct. Anal. 11 (2001), 1129
 Uniform singular continuous spectrum for the period doubling Hamiltonian, Ann. Henri
Poincare 2 (2001), 101108
 Spectral theory of Schrödinger operators with lowcomplexity potentials, Ferroelectrics
250 (2001), 143149
 Linear repetitivity, I. Uniform subadditive ergodic theorems and
applications (with Daniel Lenz), Discrete Comput. Geom. 26 (2001),
411428
 A palindromic halfline criterion for absence of eigenvalues and applications to
substitution Hamiltonians (with JeanMichel Ghez and Laurent Raymond), Ann. Henri
Poincare 2 (2001), 927939
 Local symmetries in the period doubling sequence, Discrete Appl. Math. 100
(2000), 115121
 A generalization of Gordon's theorem and applications to quasiperiodic Schrödinger
operators (with Günter Stolz), Electron. J. Diff. Eqns. 2000 (2000), No.
55, pp. 18
 Palindrome complexity bounds for primitive substitution sequences (with Douglas Zare), Discrete
Math. 222 (2000), 259267
 Substitution Hamiltonians with bounded trace map orbits, J. Math. Anal. Appl. 249
(2000), 393411
 Gordontype arguments in the spectral theory of onedimensional quasicrystals, in Directions
in Mathematical Quasicrystals, M. Baake, R. V. Moody, eds., CRM Monograph Series 13,
AMS, Providence, RI (2000), pp. 277304
 Reflection symmetries of almost periodic functions (with Rowan Killip), J. Funct.
Anal. 178 (2000), 251257
 Singular continuous spectrum for a class of substitution Hamiltonians II., Lett.
Math. Phys. 54 (2000), 2531
 Uniform spectral properties of onedimensional quasicrystals, III. alphacontinuity
(with Rowan Killip and Daniel Lenz), Commun. Math. Phys. 212 (2000), 191204
 Uniform spectral properties of onedimensional quasicrystals, II. The Lyapunov exponent
(with Daniel Lenz), Lett. Math. Phys. 50 (1999), 245257
 Uniform spectral properties of onedimensional quasicrystals, I. Absence of eigenvalues
(with Daniel Lenz), Commun. Math. Phys. 207 (1999), 687696
 Singular continuous spectrum for a class of substitution Hamiltonians, Lett. Math.
Phys. 46 (1998), 303311
 Singular continuous spectrum for the period doubling Hamiltonian on a set of full
measure, Commun. Math. Phys. 196 (1998), 477483
 alphacontinuity properties of onedimensional quasicrystals, Commun. Math. Phys.
192 (1998), 169182
Teaching
Meetings
 MiniWorkshop on Reflectionless Operators: The Deift and Simon Conjectures (with Fritz Gesztesy, Peter Yuditskii), Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, Germany (October 2228, 2017)
 Workshop on Spectral Structures and Topological Methods in Mathematical Quasicrystals (with Michael Baake, Johannes Kellendonk, Daniel Lenz), Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, Germany (October 17, 2017) webpage
 Texas Analysis and Mathematical Physics Symposium (with Thomas Chen), Rice University, Houston, USA (October 2123, 2016) webpage
 Texas Analysis and Mathematical Physics Symposium (with Thomas Chen and Vladimir Dragovic), University of Texas, Dallas, USA (November 68, 2015) webpage
 HalfWorkshop on Spectral Properties of Quasicrystals via Analysis, Dynamics, and Geometric Measure Theory (with Anton Gorodetski), Banff International Research Station, Oaxaca, Mexico (September 27October 2, 2015) webpage
 Minisymposium on Inverse Spectral Theory and Applications (with Gerald Teschl), Equadiff 2015, Lyon 1 University, France (July 610, 2015) webpage
 Program on Periodic and Ergodic Spectral Problems (with Svetlana Jitomirskaya, Frédéric Klopp, Leonid Parnovski, Alexander Sobolev), Isaac Newton Institute for Mathematical Sciences, Cambridge, UK (January 5June 26, 2015) webpage
 MiniWorkshop on Dynamical versus Diffraction Spectra in the Theory of Quasicrystals (with Michael Baake, Uwe Grimm), Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, Germany (November 30December 6, 2014) webpage
 Texas Analysis and Mathematical Physics Symposium (with Thomas Chen), University of Texas, Austin, USA (November 2123, 2014) webpage
 Special Session on Dynamical Systems and Spectral Theory, 10th AIMS International Conference on Dynamical Systems, Differential Equations and Applications, ICMAT/UAM, Madrid, Spain (July 711, 2014) webpage
 Texas Analysis and Mathematical Physics Symposium (with Thomas Chen), Rice University, Houston, USA (October 2527, 2013) webpage
 MiniWorkshop on Direct and Inverse Spectral Theory of Almost Periodic Operators (with Michael Goldstein), Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, Germany (July 2127, 2013) webpage
 Workshop on Dynamical Methods in the Spectral Theory of Quasicrystals (with Anton Gorodetski, May Mei, William Yessen), UC Irvine, Irvine, USA, (May 1619, 2013) webpage
 Recent Advances in Harmonic Analysis and Spectral Theory (with Andrew Comech, Constanze Liaw, Alexei Poltoratski), Texas A&M University, College Station, USA (August 610, 2012) webpage
 Special Session on Dynamical Systems and Spectral Theory, 9th AIMS International Conference on Dynamical Systems, Differential Equations and Applications, Hyatt Grand Cypress Resort, Orlando, USA (July 15, 2012) webpage
 Arbeitsgemeinschaft: Quasiperiodic Schrödinger Operators (with Artur Avila and Svetlana Jitomirskaya), Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, Germany (April 17, 2012) webpage
 Workshop on Almost Periodic Order: Spectral, Dynamical, and Stochastic Approaches (with Michael Baake, Daniel Lenz), Banff International Research Station, Banff, Canada (September 2530, 2011) webpage
 Minisymposium on Spectral Theory and Dynamics of Cocycles (with Roberta Fabbri), Equadiff 2011, Loughborough University, Loughborough, UK (August 15, 2011) webpage
 Special Session on Spectral Theory (with Christian Remling), Spring AMS Central Section Meeting, University of Iowa, Iowa City, USA (March 1820, 2011) webpage
 MiniWorkshop on Dynamics of Trace Maps and Applications to Spectral Theory (with Anton Gorodetski), Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, Germany (January 1622, 2011) webpage
 Texas Geometry and Topology Conference (with Alexander Bufetov, Robert Hardt), Rice University, Houston, USA (November 68, 2009) webpage
 MiniWorkshop on the Pisot Conjecture  From Substitution Dynamical Systems to Rauzy Fractals and Meyer Sets (with Valérie Berthé, Daniel Lenz), Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, Germany (March 17, 2009) webpage
 Special Session on Dynamical Systems and Spectral Theory, 7th AIMS International Conference on Dynamical Systems, Differential Equations and Applications, University of Texas, Arlington, USA (May 1821, 2008) webpage
 MiniWorkshop on the Dynamics of Cocycles and OneDimensional Spectral Theory (with Russell Johnson, Daniel Lenz), Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, Germany (Novermber 1319, 2005) webpage
 Workshop on Aperiodic Order: Dynamical Systems, Combinatorics, and Operators (with Michael Baake, Ian Putnam, Boris Solomyak), Banff International Research Station, Banff, Canada (May 29June 3, 2004) webpage
Further Items
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