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Scholarly Interest Report
         
David T. Damanik
Professor
Robert L. Moody, Sr. Chair in Mathematics; Professor of Mathematics
 
e-mail:David.T.Damanik@rice.edu
 
  • Ph.D. Mathematics (1998) Johann Wolfgang Goethe University, Frankfurt
  • M.S. Mathematics (1995) Johann Wolfgang Goethe University, Frankfurt
  • M.S. Computer Science (1996) Johann Wolfgang Goethe University, Frankfurt
 
Primary Department
   Department of Mathematics
Picture
 
Websites
 homepage
 David Damanik
 David Damanik Homepage
 
Research Areas
 Spectral Theory, Mathematical Physics, Analysis
 
Teaching Areas
 Analysis
 
Selected Publications
 Refereed articles
 

David Damanik, Anton Gorodetski "An extension of the Kunz-Souillard approach to localization in one dimension and applications to almost-periodic Schrödinger operators ." Adv. Math. , 297 (2016) : 149-173 .

 
 

David Damanik, Anton Gorodetski, William Yessen "The Fibonacci Hamiltonian ." Invent. Math. , 206 (2016) : 629-692 .

 
 

David Damanik, Jake Fillman, Darren Ong "Spreading estimates for quantum walks on the integer lattice via power-law bounds on transfer matrices ." J. Math. Pures Appl., 105 (2016) : 293-341 .

 
 

David Damanik, Jake Fillman, Milivoje Lukic, William Yessen "Characterizations of uniform hyperbolicity and spectra of CMV matrices." Discrete Contin. Dyn. Syst. S , 9 (2016) : 1009-1023 .

 
 

David Damanik, Jon Erickson, Jake Fillman, Gerhardt Hinkle, Alan Vu "Quantum intermittency for sparse CMV matrices with an application to quantum walks on the half-line." J. Approx. Theory, 208 (2016) : 59-84.

 
 

David Damanik, Marius Lemm, Milivoje Lukic, William Yessen "On anomalous Lieb-Robinson bounds for the Fibonacci XY chain ." J. Spectr. Theory, 6 (2016) : 601-628 .

 
 

David Damanik, Michael Goldstein "On the existence and uniqueness of global solutions for the KdV equation with quasi-periodic initial data." J. Amer. Math. Soc. , 29 (2016) : 825-856 .

 
 

David Damanik, Michael Goldstein, Milivoje Lukic "The spectrum of a Schrödinger operator with small quasi-periodic potential is homogeneous." J. Spectr. Theory, 6 (2016) : 415-427 .

 
 

David Damanik, Peter Yuditskii "Counterexamples to the Kotani-Last conjecture for continuum Schrödinger operators via character-automorphic Hardy spaces." Adv. Math., 293 (2016) : 738-781 .

 
 

Faustin Adiceam, David Damanik, Franz Gähler, Uwe Grimm, Alan Haynes, Antoine Julien, Andrés Navas, Lorenzo Sadun, Barak Weiss "Open problems and conjectures related to the theory of mathematical quasicrystals." Arnold Math. J., 2 (2016) : 579-592 .

 
 

Michael Baake, David Damanik, Uwe Grimm "What is ... aperiodic order?." Notices Amer. Math. Soc., 63 (2016) : 647-650 .

 
 

David Damanik, Anton Gorodetski "Almost ballistic transport for the weakly coupled Fibonacci Hamiltonian." Israel J. Math., 206 (2015) : 109-126.

 
 

David Damanik, Anton Gorodetski "Almost sure frequency independence of the dimension of the spectrum of Sturmian Hamiltonians." Commun. Math. Phys., 337 (2015) : 1241-1253.

 
 

David Damanik, Anton Gorodetski, Boris Solomyak "Absolutely continuous convolutions of singular measures and an application to the Square Fibonacci Hamiltonian." Duke Math. J., 164 (2015) : 1603-1640.

 
 

David Damanik, Anton Gorodetski, Qinghui Liu, Yanhui Qu "Transport exponents of Sturmian Hamiltonians." J. Funct. Anal., 269 (2015) : 1404-1440.

 
 

David Damanik, Jake Fillman, Milivoje Lukic, William Yessen "Uniform hyperbolicity for Szego cocycles and applications to random CMV matrices and the Ising model." Int. Math. Res. Not., 2015 (2015) : 7110-7129.

 
 

David Damanik, Milivoje Lukic, William Yessen "Quantum dynamics of periodic and limit-periodic Jacobi and block Jacobi matrices with applications to some quantum many body problems." Commun. Math. Phys., 337 (2015) : 1535-1561.

 
 

Artur Avila, David Damanik, Zhenghe Zhang "Singular density of states measure for subshift and quasi-periodic Schr\"odinger operators." Commun. Math. Phys., 330 (2014) : 469-498.

 
 

David Damanik, Anton Gorodetski "Almost ballistic transport for the weakly coupled Fibonacci Hamiltonian." Israel J. Math. (2014)

 
 

David Damanik, Jake Fillman and Robert Vance, Dynamics of unitary operators, J. Fract. Geom. 1 (2014), 391–425

 
 

David Damanik, Jake Fillman, Anton Gorodetski "Continuum Schr\"odinger operators associated with aperiodic subshifts." Ann. Henri Poincar\'e, 15 (2014) : 1123-1144.

 
 

David Damanik, Marius Lemm, Milivoje Lukic, William Yessen "New anomalous Lieb-Robinson bounds in quasiperiodic XY chains." Phys. Rev. Lett., 113 (2014)

 
 

David Damanik, Michael Goldstein "On the inverse spectral problem for the quasi-periodic Schr\"odinger equation." Publ. Math. Inst. Hautes Études Sci., 119 (2014) : 217-401.

 
 

David Damanik, Michael Goldstein "On the inverse spectral problem for the quasi-periodic Schr\"odinger equation." Publ. Math. Inst. Hautes Études Sci., 119 (2014) : 217-401.

 
 

David Damanik, Anton Gorodetski, H\"older continuity of the integrated density of states for the Fibonacci Hamiltonian, Commun. Math. Phys. 323 (2013), 497--515


http://link.springer.com/article/10.1007%2Fs00220-013-1753-7
 
 

David Damanik, Paul Munger, William Yessen, Orthogonal polynomials on the unit circle with Fibonacci Verblunsky coefficients, I. The essential support of the measure, J. Approx. Theory 173 (2013), 56–-88


http://www.sciencedirect.com/science/article/pii/S0021904513000671
 
 

David Damanik, Paul Munger, William Yessen, Orthogonal polynomials on the unit circle with Fibonacci Verblunsky coefficients, II. Applications, J. Stat. Phys. 153 (2013), 339--362


http://link.springer.com/article/10.1007%2Fs10955-013-0830-9
 
 

David Damanik, Zheng Gan, Limit-periodic Schr\"odinger operators on $\mathbb{Z}^d$: Uniform localization, J. Funct. Anal. 265 (2013), 435--448


http://www.sciencedirect.com/science/article/pii/S0022123613001651
 
 

Artur Avila, Jairo Bochi, David Damanik "Opening gaps in the spectrum of strictly ergodic Schrödinger operators." J. Eur. Math. Soc., 14 (2012) : 61–106.

 
 

David Damanik, Anton Gorodetski "The density of states measure of the weakly coupled Fibonacci Hamiltonian." Geom. Funct. Anal., 22 (2012) : 976-989 .

 
 

David Damanik, Anton Gorodetski, Spectral and quantum dynamical properties of the weakly coupled Fibonacci Hamiltonian, Commun. Math. Phys. 305 (2011), 221–-277

 
 

David Damanik, Gunter Stolz, A continuum version of the Kunz-Souillard approach to localization in one dimension, J. Reine Angew. Math. 660 (2011), 99–-130

 
 

David Damanik, Zheng Gan, Limit-periodic Schodinger operators with uniformly localized eigenfunctions, J. d'Analyse Math. 115 (2011), 33–-49

 
 

David Damanik, Zheng Gan, Spectral properties of limit-periodic Schrodinger operators, Commun. Pure Appl. Anal. 10 (2011), 859--871

 
 

David Damanik, Rowan Killip, Barry Simon, Perturbations of orthogonal polynomials with periodic recursion coeffcients, Ann. of Math. 171 (2010), 1931-2010

 
 

David Damanik, Serguei Tcheremchantsev, A general description of quantum dynamical spreading over an orthonormal basis and applications to Schrodinger operators, Discrete Contin. Dyn. Syst. A
28 (2010), 1381-1412

 
 

David Damanik, Zheng Gan, Limit-periodic Schrodinger operators in the regime of positive Lyapunov exponents, J. Funct. Anal. 258 (2010), 4010-4025

 
 

Artur Avila, Jairo Bochi, David Damanik, Cantor spectrum for Schr\"odinger operators with potentials arising from generalized skew-shifts, Duke Math. J. 146 (2009), 253--280

 
 

Artur Avila, Jairo Bochi, David Damanik, Opening gaps in the spectrum of strictly ergodic
Schr\"odinger operators

 
 

David Damanik, Anton Gorodetski, Hyperbolicity of the trace map for the weakly coupled Fibonacci Hamiltonian, Nonlinearity 22 (2009), 123--143

 
 

David Damanik, Anton Gorodetski, The spectrum of the weakly coupled Fibonacci Hamiltonian, Electron. Res. Announc. Math. Sci. 16 (2009), 23--29

 
 

David Damanik, G\"unter Stolz, A continuum version of the Kunz-Souillard approach to localization in one dimension

 
 

David Damanik, Helge Kr\"uger, Almost periodic Szeg\H{o} cocycles with uniformly positive Lyapunov exponents, J. Approx. Theory 161 (2009), 813--818

 
 

David Damanik, Jon Chaika, Helge Kr\"uger, Schr\"odinger operators defined by interval exchange transformations, J. Mod. Dyn. 3 (2009), 253--270

 
 

David Damanik, Rafael del Rio, Quantum dynamical applications of Salem's theorem, Lett. Math. Phys. 89 (2009), 13--19

 
 

David Damanik, Zheng Gan, Limit-periodic Schr\"{o}dinger operators in the regime of
positive Lyapunov exponents

 
 

Michael Boshernitzan, David Damanik, Pinned repetitions in symbolic flows: preliminary results, to appear in Discrete Contin. Dyn. Syst.

 
 

Artur Avila, David Damanik "Absolute continuity of the integrated density of states for the almost Mathieu operator with non-critical coupling." Inventiones Mathematicae, 172 (2008) : 439-453.

 
 

David Damanik, Alexander Pushnitski, Barry Simon "The analytic theory of matrix orthogonal polynomials." Surveys in Approximation Theory, 4 (2008) : 1-85.

 
 

David Damanik, Anton Gorodetski "The spectrum and the spectral type of the off-diagonal Fibonacci operator." Submitted

 
 

David Damanik, Kristian Bjerkl\"ov, Russell Johnson "Lyapunov exponents of continuous Schr\"odinger cocycles over irrational rotations." Annali di Matematica Pura ed Applicata, 187 (2008) : 1-6.

 
 

David Damanik, Mark Embree, Anton Gorodetski, Serguei Tcheremchantsev "The fractal dimension of the spectrum of the Fibonacci Hamiltonian." Communications in Mathematical Physics, 280 (2008) : 499-516.

 
 

David Damanik, Rowan Killip, Barry Simon "Perturbations of orthogonal polynomials with periodic recursion coefficients." Annals of MathematicsIn Press

 
 

David Damanik, Serguei Tcheremchantsev "Quantum dynamics via complex analysis methods: General upper bounds without time-averaging and tight lower bounds for the strongly coupled Fibonacci Hamiltonian." Journal of Functional Analysis, 255 (2008) : 2872-2887.

 
 

Michael Boshernitzan, David Damanik "Generic continuous spectrum for ergodic Schr\"odinger operators." Communications in Mathematical Physics, 283 (2008) : 647-662.

 
 

Michael Boshernitzan, David Damanik "The repetition property for sequences on tori generated by polynomials or skew-shifts." Isael Journal of MathematicsIn Press

 
 

David Damanik, Artur Avila "Absolute continiuty of the integrated density of states for the almost Mathieu operator with non-critical coupling." Invent. Math.In Press

 
 

David Damanik, Christian Remling "Schrödinger operators with many bound states." Duke Math. J., 136 (2007) : 51-80.

 
 

David Damanik, Daniel Lenz "Uniform Szegö cocycles over strictly ergodic subshifts." J. Approx. Theory, 144 (2007) : 133-138.

 
 

David Damanik, Gerald Teschl "Bound states of discrete Schrödinger operators with super-critical inverse square potentials." Proc. Amer. Math. Soc., 135 (2007) : 1123-1127.

 
 

David Damanik, Kristian Bjerkloev, Russell Johnson "Lyapunov exponents of continuous Schroedinger cocycles over irrational rotations." Ann. Mat. Pura. Appl.In Press

 
 

David Damanik, Sergey Naboko "Unbounded Jacobi matrices at critical coupling." J. Approx. Theory, 145 (2007) : 221-236.

 
 

David Damanik, Serguei Tcheremchantsev "Upper bounds in quantum dynamics." J. Amer. Math. Soc., 20 (2007) : 799-827.

 
 

David Damanik "Verblunsky coefficients with Coulomb-type decay." Journal of Approximation Theory, 139 (2006) : 257-268.

 
 

David Damanik, Barry Simon "Jost functions and Jost solutions for Jacobi matrices, I. A necessary and sufficient condition for Szegö asymptotics." Inventiones Mathematicae, 165 (2006) : 1-50.

 
 

David Damanik, Barry Simon "Jost functions and Jost solutions for Jacobi matrices, II. Decay and analyticity." International Mathematical Research Notices, 2006 (2006)

 
 

David Damanik, Daniel Lenz "A criterion of Boshernitzan and uniform convergence in the multiplicative ergodic theorem." Duke Mathematical Journal, 133 (2006) : 95-123.

 
 

David Damanik, Daniel Lenz "Substitution dynamical systems: characterization of linear repetitivity and applications." Journal of Mathematical Analysis and Applications, 321 (2006) : 766-780.

 
 

David Damanik, Daniel Lenz "Zero-measure Cantor spectrum for Schrödinger operators with low-complexity potentials." Journal de Mathematiques Pures et Appliquees, 85 (2006) : 671-686.

 
 

David Damanik, Daniel Lenz, Gunter Stolz "Lower transport bounds for one-dimensional continuum Schrödinger operators." Mathematische Annalen, 336 (2006) : 361-389.

 
 Book chapters
 

David Damanik, Mark Embree, Anton Gorodetski "Spectral properties of Schr\"odinger operators arising in the study of quasicrystals." Mathematics of Aperiodic Order (2015) : 307-370.

 
 Refereed conference papers
 

David Damanik "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 (2007) : 539--563.

 
 

David Damanik "Strictly ergodic subshifts and associated operators." Spectral theory and mathematical physics: a Festschrift in honor of Barry Simon's 60th birthday (2007) : 505--538.

 
 Conference papers
 

David Damanik "Almost everything about the Fibonacci operator." ICMP 2006 ProceedingsIn Press

 
Presentations
 Invited Talks
 

"Almost Periodicity in Time of Solutions of the KdV Equation." Texas Geometry-Topology Conference, Fort Worth. (02/20/16)

 
 

"Almost Periodicity in Time of Solutions of the KdV Equation." Mathematical Physics of Quasi-periodic Systems and Related Topics, Kyoto. (11/08/16)

 
 

"Aperiodic order: Schr"odinger operators." Dynamical Systems for Aperiodicity, Lyon. (01/07/16)

 
 

"Quantum Transport in Quasicrystalline Environments." Between Dynamics and Spectral Theory, Stony Brook. (06/08/16)

 
 

"Some recent progress in the study of quasi-periodic Schrödinger operators I.." Mathematical Physics of Quasi-periodic Systems and Related Topics, Kyoto. (11/07/16)

 
 

"Some recent progress in the study of quasi-periodic Schrödinger operators II.." Mathematical Physics of Quasi-periodic Systems and Related Topics, Kyoto. (11/08/16)

 
 

"The spectrum of the continuum Fibonacci Hamiltonian." Spectral Theory of Periodic, Quasi-periodic, and Random Problems, London. (06/05/16)

 
 

Schr\"odinger spectrum and quantum dynamics, Mini-Workshop on ``Dynamical versus Diffraction Spectra in the Theory of Quasicrystals,'' MFO, Oberwolfach, Germany, December 1, 2014

 
 

The Boshernitzan condition and Simon's subshift conjecture, Wasatch Topology Conference, University of Utah, Salt Lake City, USA, November 16, 2014

 
 

The spectrum and the density of states measure of the Fibonacci Hamiltonian, AMS-Meeting #1099$, Special Session on Hyperbolic Dynamics, Dynamically Defined Fractals, and Applications, University of New Mexico, Albuquerque, USA, April 5, 2014

 
 

Transport exponents associated with the Fibonacci Hamiltonian, AMS-Meeting #1099$, Special Session on Spectral Theory, University of New Mexico, Albuquerque, USA, April 5, 2014

 
 

Uniform hyperbolicity for Szego cocycles and applications to random CMV matrices and the Ising model, Workshop on ``Komplexe Analysis und/et Th\'eorie Spectrale,'' Johannes Kepler Universit\"at, Linz, Austria, May 12, 2014

 
 

Spectral analysis of Jacobi matrices, mini-course (series of nineteen 60-minute lectures), Nanjing University, Nanjing, China, April 10--26, 2013

 
 

The Fibonacci Hamiltonian: spectrum, density of states measure, and transport exponents, Mathematics in the Natural Sciences Seminar, Universit\"at Bielefeld, Bielefeld, Germany, July 15, 2013

 
 

The spectrum of quasi-periodic Schr\"odinger operators in the perturbative regime, Conference on ``Dissipative Spectral Theory: Operator Theory, PDEs and Numerics,'' Cardiff School of Mathematics, Cardiff University, Cardiff, UK, January 10, 2013

 
 

Zero-measure spectrum vs. singular IDS, Western States Mathematical Physics Meeting, Caltech, Pasadena, USA, February 19, 2013

 
 

Dynamical Systems Seminar, University of California, Irvine, USA, June 1, 2012

 
 

Mathematics in the Natural Sciences Seminar, Universitaet Bielefeld, Bielefeld, Germany, August 15, 2012

 
 

Forschungsseminar Analysis, Stochastik und Mathematische Physik, TU Chemnitz, Chemnitz, Germany, August 8, 2012

 
 

Pure Mathematics Colloquium, University of St. Andrews, St. Andrews, Scotland, June 27, 2012

 
 

Mathematics Colloquium, University of Arkansas, Fayetteville, January 19, 2012

 
 

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 3, 2012

 
 

Conference on ``Dynamics and PDEs,'' Centre International de Rencontres Mathematiques, Luminy, France, November 12, 2012

 
 

AMS-Meeting #1080, George Washington University, Washington, DC, USA, March 17, 2012

 
 

Mathematics Colloquium, University of Illinois, Chicago, USA, April 20, 2012

 
 

Mathematical Physics and Harmonic Analysis Seminar, Texas A&M University, College Station, USA, March 23, 2012

 
 

Workshop on ``Periodic Orbits in Dynamical Systems,'' ESI, Vienna, Austria, May 24, 2012

 
 

Analysis Seminar, University of St. Andrews, St. Andrews, Scotland, June 26, 2012

 
 

"Anderson localization in the presence of correlations." Mathematical Physics Colloquium, Universitat Bielefeld, Bielefeld, Germany. (June 11, 2010)

 
 

"Aperiodic order and quantum mechanics." Workshop on ``The Mathematics of Aperiodic Order'', KIAS, Seoul, Korea. (October 1, 2010)

 
 

"Cantor spectra and gap labeling." Mathematical Physics Seminar, University of Texas, Austin, USA. (May 5, 2010)

 
 

"Correlated random potentials." Conference on ``Random Schr\"odinger Operators,'' Program on ``Spectral and Dynamical Properties of Quantum Hamiltonians'', Centre Interfacultaire Bernoulli, EPFL, Lausanne, Switzerland. (June 3, 2010)

 
 

"Dynamical aspects of the spectral analysis of Schrodinger operators." Workshop on ``Non-Uniform Hyperbolicity and Interval Exchange Maps,'' Program on ``Dynamics and PDE's, Institut Mittag-Leffler, Stockholm, Sweden. (April 7, 2010)

 
 

"Pseudo-randomness and orthogonal polynomials." Workshop on ``Orthogonal Polynomials in Probability Theory'', Texas A&M University, College Station, USA. (July 9, 2010)

 
 

"Schrodinger operators with dynamically defined potentials." Fractal Geometry Seminar, Tsinghua University, Beijing, China. (July 16, 2010)

 
 

"Schrodinger operators with limit-periodic potentials." Forschungsseminar Analysis und Mathematische Physik, TU Chemnitz, Chemnitz, Germany. (June 16, 2010)

 
 

"Schrodinger operators with limit-periodic potentials." Oberseminar Geometrie, Friedrich-Schiller-Universitat, Jena, Germany. (June 15, 2010)

 
 

"Spectral dimensions and transport exponents." PDE Seminar, University of Houston, Houston, USA. (March 26, 2010)

 
 

"The Fibonacci Hamiltonian." Dynamical Systems Seminar, University of Houston, Houston, USA. (April 23, 2010)

 
 

"The Square Fibonacci Hamiltonian and arithmetic sums of Cantor sets." Fall 2010 SCAPDE, University of California, Los Angeles, USA. (November 14, 2010)

 
 

"The Square Fibonacci Hamiltonian and arithmetic sums of Cantor sets." Mathematics Colloquium, University of Oklahoma, Norman, USA. (October 21, 2010)

 
 

"What determines the spreading of a wavepacket?." Workshop on ``Dynamics and PDE's,'' Program on ``Dynamics and PDE's, Institut Mittag-Leffler, Stockholm, Sweden. (May 27, 2010)

 
 

"Cantor spectra and gap labeling." Mathematics Colloquium, University of Alabama, Birmingham. (October 9, 2009)

 
 

"Dynamics of SL$(2,\mathbb{R})$-cocycles and applications to spectral theory." Workshop on ``Global Dynamics Beyond Uniform Hyperbolicity'', Peking University, Beijing, China. (August 10--13, 2009)

 
 

"Aperiodic order and anomalous transport." Workshop on Aspects of Aperiodic Order, Universit\"at Bielefeld, Bielefeld. (July 3, 2008)

 
 

"Coefficient stripping and sum rules for Jacobi matrices." Free Probability Seminar, Texas A&M University, College Station. (November 14, 2008)

 
 

"Critical eigenstates, spectral dimensions, and anomalous transport." CAMP/Nonlinear PDE Seminar, University of Chicago, Chicago. (January 23, 2008)

 
 

"Critical eigenstates, spectral dimensions, and anomalous transport." Mathematics Colloquium, University of Oklahoma, Norman. (January 17, 2008)

 
 

"Lyapunov exponents of Schr\"odinger cocycles and the Kotani-Last conjecture." 19th Fall Meeting of the Workshop in Dynamical Systems and Related Topics, Penn State University, State College. (October 25, 2008)

 
 

"Schr\"odinger cocycles over the skew-shift." Dynamical Systems Seminar, Northwestern University, Evanston. (October 28, 2008)

 
 

"Schr\"odinger cocycles over the skew-shift." Dynamical Systems Seminar, University of Maryland, College Park. (November 6, 2008)

 
 

"Schr\"odinger cocycles over the skew-shift." UNAM, Mexico City. (November 24. 2008)

 
 

"Schr\"odinger operators with dynamically defined potentials." Mathematics Colloquium, PUC-Rio, Rio de Janeiro. (August 6, 2008)

 
 

"Schr\"odinger operators with potentials generated by low-complexity dynamical systems." Workshop on Low Complexity Dynamics, BIRS, Banff. (May 29, 2008)

 
 

"Schr\"odinger operators with potentials generated by the skew-shift." AIMS Seventh International Conference on Dynamical Systems, Differential Equations and Applications, University of Texas, Arlington. (May 19, 2008)

 
 

"Singular spectrum for Schr\"odinger operators generated by interval exchange transformations." Mathematical Physics Seminar, University of California, Irvine. (September 25, 2008)

 
 

"Some aspects of the mathematics of quasicrystals." Mathematics Colloquium, Western Michigan University, Kalamazoo. (February 7, 2008)

 
 

"Spectral dimensions and transport exponents." Conference on Operator Methods and Applications in Mathematical Physics, Bedlewo, Poland. (June 19, 2008)

 
 

"The fractal dimension of the spectrum of the Fibonacci Hamiltonian." Analysis and Convexity Seminar, University of Oklahoma, Norman. (January 14, 2008)

 
 

"The fractal dimension of the spectrum of the Fibonacci Hamiltonian." Analysis Seminar, Western Michigan University, Kalamazoo. (February 6, 2008)

 
 

"The repetition property and applications to spectral theory." London Analysis and Probability Seminar, King's College, London. (December 11, 2008)

 
 

"The repetition property and applications to spectral theory." Thematic Program on New Trends in Harmonic Analysis, Fields Institute, Toronto. (May 8, 2008)

 
 

"The skew-shift model and pseudo-randomness from a spectral perspective." Workshop on Disordered Systems: Random Schr\"odinger Operators and Random Matrices, MFO, Oberwolfach. (March 24, 2008)

 
 

"The spectrum of the almost Mathieu operator." Lecture Series (series of six 75-minute lectures), Universit\"at Bielefeld, Bielefeld. (June 11-July 4, 2008)

 
 

"Hyperbolicity, fractal dimension, and quantum dynamics for the Fibonacci Hamiltonian." Workshop on ``Transport in Multi-Dimensional Random Schroedinger Operators, Oberwolfach, Germany. (March 6, 2007)

 
 

"The subcritical almost Mathieu operator." Western States Mathematical Physics Meeting, Caltech, Pasadena, USA. (February 20, 2007)

 
 

"Dominated Schroedinger Cocycles." Transport Properties of Random Schroedinger Operators, University of Kentucky, Lexington, USA. (18 Mar 2006)

 
 

"Lyapunov exponents and spectral analysis of ergodic Schroedinger operators." Spectral Theory and Mathematical Physics, California Institute of Technology, Pasadena, USA. (30 Mar 2006)

 
 

"Lyapunov exponents of deterministic products of matrices arising in the study of Schroedinger operators." Spectral Theory of Random Operators and Related Fields in Probability Theory, Kyoto University, Kyoto, Japan. (12 Dec 2006)

 
 

"Quantum dynamics for the Fibonacci Hamiltonian." Journee Dynamique, Univesite de Paris VI/VII, Paris, France. (24 Nov 2006)

 
 

"Recent applications of Kotani theory." Spectral Theory of Random Operators and Related Fields in Probability Theory, Kyoto University, Kyoto, Japan. (13 Dec 2006)

 
 

"Recent progress in the spectral theory of quasi-periodic operators." ICMP 2006, Rio de Janeiro. (7 Aug 2006)

 
 Keynote Speaker
 

Invited one-hour address, AMS 2011 Spring Central Section Meeting, University of Iowa, Iowa City, USA, March 19, 2011

 
 

Plenary lecture, Equadiff 2011, Loughborough University, Loughborough, UK, August 2, 2011

 
 

"Ergodic Schrodinger operators." School on Information and Randomness, Pucon, Chile. (December 10, 2010)

 
 

"Non-uniformly hyperbolic Schrodinger equations." Non-Uniformly Hyperbolic Days, Pontificia Universidad Cat\'olica de Chile, Santiago, Chile. (January 18, 2010)

 
 Lectures
 

Cantor sets and Cantor measures, Oberseminar Geometrie, Friedrich-Schiller-Universit\"at, Jena, Germany, January 10, 2014

 
 

Cantor sets and Cantor measures, Mathematics Colloquium, University of California, Irvine, USA, April 3, 2014

 
 

Cantor sets and Cantor measures, Mathematics Colloquium, University of Utah, Salt Lake City, USA, April 10, 2014

 
 

Cantor sets and Cantor measures, Mathematics Colloquium, Baylor University, Waco, USA, March 24, 2014

 
 

Cantor sets and Cantor measures, Mathematics Colloquium, TU Chemnitz, Chemnitz, Germany, January 9, 2014

 
 

Trace map dynamics and spectral properties of the Fibonacci Hamiltonian, joint mini-course with Anton Gorodetski (series of four 60-minute lectures), Workshop on ``Dynamical Methods in the Spectral Theory of Quasicrystals,'' University of California, Irvine, USA, May 16--19, 2013

 
 

Mathematics Colloquium, Williams College, Williamstown, USA, May 6, 2011

 
 

Mini-Course (series of five 60-minute lectures), University College, London, UK, June 26 - July 1, 2011

 
 

"Connections between discrete eigenvalues and embedded singular spectra." Universitaet Bielefeld, Bielefeld, Germany. (July 5, 2007)

 
 

"Generic phenomena for ergodic Schr\"odinger operators." Universita di Firenze, Florence, Italy. (June 26, 2007)

 
 

"Spectra and spectral types of quasiperiodic Schr\"odinger operators." TU Chemnitz, Chemnitz, Germany. (June 14, 2007)

 
 

"Spectra and spectral types of quasiperiodic Schr\"odinger operators." Ruhr-Universitaet, Bochum, Germany. (June 19, 2007)

 
 

"Spectra and spectral types of quasiperiodic Schr\"odinger operators." Johann Wolfgang Goethe Universitaet, Frankfurt, Germany. (June 20, 2007)

 
 

"The fractal dimension of the spectrum of the Fibonacci operator." IIMA, UNAM, Mexico City, Mexico. (May 8, 2007)

 
 

"The subcritical almost Mathieu operator." UAB, Birmingham, USA. (March 30, 2007)

 
 

"The subcritical almost Mathieu operator." Friedrich-Alexander-Universitaet, Erlangen-Nuernberg, Germany. (Juli 12, 2007)

 
 Seminar Speaker
 

"Almost Periodicity in Time of Solutions of the KdV Equation." Colloquium, Blacksburg. (04/01/16)

 
 

"Almost Periodicity in Time of Solutions of the KdV Equation." Mathematical Physics Seminar, Tokyo. (11/05/16)

 
 

"Almost Periodicity in Time of Solutions of the KdV Equation." Analysis Seminar, Jena. (04/14/16)

 
 

"Quantum Transport in Quasicrystalline Environments." Mathematical Physics Seminar, Munich. (06/14/16)

 
 

"Almost-periodic continuum Schr\"odinger operators with zero measure Cantor spectrum, Mathematics in the Natural Sciences Seminar, Universit\"at Bielefeld, Bielefeld, Germany." (July 17, 2015)

 
 

"An extension of the Kunz-Souillard approach to localization in one dimension, Mathematics in the Natural Sciences Seminar, Universit\"at Bielefeld, Bielefeld, Germany." (November 11, 2015)

 
 

"Pure point spectrum in the regime of zero Lyapunov exponents, Dynamical Systems Seminar, University of Maryland, College Park, USA." (April 30, 2015)

 
 

"Pure point spectrum in the regime of zero Lyapunov exponents, Fractal Geometry Seminar, Tsinghua University, Beijing, China." (May 12, 2015)

 
 

"The KdV equation with almost periodic initial data, Mathematics Colloquium, University of Alabama, Birmingham, USA." (September 11, 2015)

 
 

Fractional Lieb-Robinson bounds, Arbeitsgemeinschaft Mathematische Physik, Friedrich-Alexander-Universit\"at, Erlangen, Germany, July 17, 2014

 
 

The Boshernitzan condition and Simon's subshift conjecture, Fractal Geometry Seminar, Tsinghua University, Beijing, China, October 14, 2014

 
 

An introduction to the spectral decimation method, Dynamical Systems Seminar, University of California, Irvine, USA, January 29, 2013

 
 

Dynamical Systems Seminar, University of California, Irvine, USA, December 2, 2011

 
 

Analysis and Randomness Seminar, Ludwig-Maximilians-Universitat, Munich, Germany, July 5, 2011

 
 

Arbeitsgemeinschaft Mathematische Physik, Friedrich-Alexander-Universitat, Erlangen, Germany, July 7, 2011

 
 

Ergodic Theory and Dynamical Systems Seminar, University of California, Irvine, USA, May 16, 2011

 
 

Analysis Seminar, University of Wisconsin, Madison, USA, March 22, 2011

 
 

Functional Analysis Seminar, University of Tokyo, Tokyo, Japan, February 23, 2011

 
 

"Cantor groups and limit-periodic Schr\"odinger operators." Mathematics in the Natural Sciences Seminar, Universit\"at Bielefeld, Bielefeld, Germany. (May 22, 2009)

 
 

"Cantor groups and limit-periodic Schr\"odinger operators." Mathematical Physics Seminar, Ludwig-Maximilians-Universit\"at, M\"unchen, Germany. (May 15, 2009)

 
 

"Pseudorandom potentials: open problems and some recent results." Mathematical Physics and Harmonic Analysis Seminar, Texas A&M University, College Station. (April 17, 2009)

 
 

"Generic phenomena for ergodic Schr\"odinger operators." Ludwig-Maximilians-Universitaet, Munich, Germany. (July 13, 2007)

 
 

"Spectra and spectral types of quasiperiodic Schr\"odinger operators." Universitaet Bielefeld, Bielefeld, Germany. (July 2, 2007)

 
 

"The fractal dimension of the spectrum of the Fibonacci Hamiltonian." UAB, Birmingham, USA. (March 30, 2007)

 
 

"The fractal dimension of the spectrum of the Fibonacci operator." Penn State University, State College, USA. (April 18, 2007)

 
 

"The subcritical almost Mathieu operator." University of Houston, Houston, USA. (March 23, 2007)

 
 

"The subcritical almost Mathieu operator." Texas A&M University, College Station, USA. (April 13, 2007)

 
 

"Wavepacket spreading on the Fibonacci chain." Caltech, Pasadena, USA. (February 7, 2007)

 
 

"Wavepacket spreading on the Fibonacci chain." UC Irvine, Irvine, USA. (February 8, 2007)

 
 Workshops
 

"General spectral properties of ergodic operators, mini-course (series of four 60-minute lectures), ``Periodic, Almost-Periodic, and Random Operators: Instructional School,'' Isaac Newton Institute for Mathematical Sciences, Cambridge, UK." (January 5-7, 2015)

 
 

"Pure point spectrum in the regime of zero Lyapunov exponents, Workshop on ``Random and other ergodic problems'' within the 6 month programme ``Periodic and Ergodic Spectral Problems,'' Isaac Newton Institute for Mathematical Sciences, Cambridge, UK." (June 24, 2015)

 
 

"Quasicrystals: from a spectral theorist's perspective, Workshop on ``Spectral Properties of Quasicrystals via Analysis, Dynamics, and Geometric Measure Theory,'' Banff International Research Station, Oaxaca, Mexico." (September 28, 2015)

 
 

"Spectral properties of quasi-periodic Schr\"odinger operators and applications, AMS-Meeting #1114, Special Session on ``Spectral Theory of Ergodic Schr\"odinger Operators and Related Models,'' California State University, Fullerton, USA." (October 24, 2015)

 
 

Mini-Workshop on ``Dynamics of Trace Maps and Applications to Spectral Theory,'' MFO, Oberwolfach, Germany, January 18, 2011

 
 

Workshop on ``Spectral and Scattering Theory and Related Topics,'' RIMS, Kyoto, Japan, February 17, 2011

 
 

Workshop on ``Waves and Spectra,'' Texas A&M University, College Station, USA, January 11, 2011

 
 

"Correlated random potentials and dominated Schr\"odinger cocycles." Modeling and Understanding Random Hamiltonians: Beyond Monotonicity, Linearity and Independence, MFO, Oberwolfach, Germany. (December 11, 2009)

 
 

"Pseudorandom potentials: open problems and some recent results." Random Schr\"odinger Operators: Universal Localization, Correlations, and Interactions, BIRS, Banff, Canada. (April 22, 2009)

 
 

"Schr\"odinger operators with potentials generated by substitutions." The Pisot Conjecture - From Substitution Dynamical Systems to Rauzy Fractals and Meyer Sets, MFO, Oberwolfach. (March 4, 2009)

 
Supervised Theses & Dissertations
 Helge Krueger, Ph. D. Positive Lyapunov Exponent for Ergodic Schr¨odinger Operators. (2010) (Thesis Director)

 Janine Dahl, Ph. D. The Spectrum of the O -diagonal Fibonacci Operator. (2011) (Thesis Director)

 Zheng Gan, Ph.D. Spectral Properties of Limit-Periodic Schrodinger Operators. (2012) (Thesis Director)

 Zheng Gan, Ph. D. Limit-Periodic Schr¨odinger Operators. (2012) (Thesis Director)

 Paul Munger, Ph.D. Spectral theory of Fibonacci operators. (2014) (Thesis Director)

 Darren Ong, Ph.D. OPUC and CMV matrices. (2014) (Thesis Director)

 Darren Ong, Ph.D. OPUC with almost periodic Verblunsky coefficients. (2014) (Thesis Director)

 Darren Ong, Ph. D. Spectral characteristics of aperiodic CMV and Schrödinger operators. (2014) (Thesis Director)

 Paul Munger, Ph.D. Spectral theory of Fibonacci operators. (2014) (Thesis Director)

 Paul Munger, Ph. D. Spectral Regularity in Models of Aperiodic Order. (2014) (Thesis Director)

 Jake Fillman, Ph. D. Spectral Theory. (2015) (Thesis Director)

 Jacob Fillman, Ph.D. Spectral Theory. (2015) (Thesis Director)

 Jacob Fillman, Ph.D. Spectral theory. (2015) (Thesis Director)

 Jacob Fillman, Ph. D. Spectral Analysis of One-Dimensional Operators. (2015) (Thesis Director)

 Valmir Bucaj, Ph. D. Spectral Theory. (2018) (Thesis Director)

 Valmir Bucaj, Ph. D. Spectral Theory. (2018) (Thesis Director)

 Tom VandenBoom, Ph. D. Spectral Theory. (2018) (Thesis Director)

 Vitalii Gerbuz, Ph. D. Spectral Theory. (2018) (Thesis Director)

 Vitalii Gerbuz, Ph. D. Spectral Theory. (2018) (Thesis Director)

 Tom VandenBoom, Ph. D. Spectral Theory. (2018) (Thesis Director)

 Eric Hintikka, Ph. D. Spectral Theory. (2019) (Thesis Director)

 Hyunkyu Jun, Ph. D. Spectral Theory. (2020) (Thesis Director)

Awards, Prizes, & Fellowships
 Simons Fellowship, Simons Foundation (July 1, 2012)

 Dynamics of Schroedinger Cocycles and Applications to Spectral Theory, National Science Foundation (September 1, 2008)

 Positive Lyapunov Exponents for Schroedinger Cocycles, National Science Foundation (15 Sep 2006)