Scholarly Interest Report


 

David T. Damanik  Professor  Robert L. Moody, Sr. Chair in Mathematics; Professor of Mathematics   email: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    
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 KunzSouillard approach to localization in one dimension and applications to almostperiodic Schrödinger operators ." Adv. Math. , 297 (2016) : 149173 .    David Damanik, Anton Gorodetski, William Yessen "The Fibonacci Hamiltonian ." Invent. Math. , 206 (2016) : 629692 .    David Damanik, Jake Fillman, Darren Ong "Spreading estimates for quantum walks on the integer lattice via powerlaw bounds on transfer matrices ." J. Math. Pures Appl., 105 (2016) : 293341 .    David Damanik, Jake Fillman, Milivoje Lukic, William Yessen "Characterizations of uniform hyperbolicity and spectra of CMV matrices." Discrete Contin. Dyn. Syst. S , 9 (2016) : 10091023 .    David Damanik, Jon Erickson, Jake Fillman, Gerhardt Hinkle, Alan Vu "Quantum intermittency for sparse CMV matrices with an application to quantum walks on the halfline." J. Approx. Theory, 208 (2016) : 5984.    David Damanik, Marius Lemm, Milivoje Lukic, William Yessen "On anomalous LiebRobinson bounds for the Fibonacci XY chain ." J. Spectr. Theory, 6 (2016) : 601628 .    David Damanik, Michael Goldstein "On the existence and uniqueness of global solutions for the KdV equation with quasiperiodic initial data." J. Amer. Math. Soc. , 29 (2016) : 825856 .    David Damanik, Michael Goldstein, Milivoje Lukic "The spectrum of a Schrödinger operator with small quasiperiodic potential is homogeneous." J. Spectr. Theory, 6 (2016) : 415427 .    David Damanik, Peter Yuditskii "Counterexamples to the KotaniLast conjecture for continuum Schrödinger operators via characterautomorphic Hardy spaces." Adv. Math., 293 (2016) : 738781 .    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) : 579592 .    Michael Baake, David Damanik, Uwe Grimm "What is ... aperiodic order?." Notices Amer. Math. Soc., 63 (2016) : 647650 .    David Damanik, Anton Gorodetski "Almost ballistic transport for the weakly coupled Fibonacci Hamiltonian." Israel J. Math., 206 (2015) : 109126.    David Damanik, Anton Gorodetski "Almost sure frequency independence of the dimension of the spectrum of Sturmian Hamiltonians." Commun. Math. Phys., 337 (2015) : 12411253.    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) : 16031640.    David Damanik, Anton Gorodetski, Qinghui Liu, Yanhui Qu "Transport exponents of Sturmian Hamiltonians." J. Funct. Anal., 269 (2015) : 14041440.    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) : 71107129.    David Damanik, Milivoje Lukic, William Yessen "Quantum dynamics of periodic and limitperiodic Jacobi and block Jacobi matrices with applications to some quantum many body problems." Commun. Math. Phys., 337 (2015) : 15351561.    Artur Avila, David Damanik, Zhenghe Zhang "Singular density of states measure for subshift and quasiperiodic Schr\"odinger operators." Commun. Math. Phys., 330 (2014) : 469498.    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) : 11231144.    David Damanik, Marius Lemm, Milivoje Lukic, William Yessen "New anomalous LiebRobinson bounds in quasiperiodic XY chains." Phys. Rev. Lett., 113 (2014)    David Damanik, Michael Goldstein "On the inverse spectral problem for the quasiperiodic Schr\"odinger equation." Publ. Math. Inst. Hautes Études Sci., 119 (2014) : 217401.    David Damanik, Michael Goldstein "On the inverse spectral problem for the quasiperiodic Schr\"odinger equation." Publ. Math. Inst. Hautes Études Sci., 119 (2014) : 217401.    David Damanik, Anton Gorodetski, H\"older continuity of the integrated density of states for the Fibonacci Hamiltonian, Commun. Math. Phys. 323 (2013), 497515 http://link.springer.com/article/10.1007%2Fs0022001317537    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), 339362 http://link.springer.com/article/10.1007%2Fs1095501308309    David Damanik, Zheng Gan, Limitperiodic Schr\"odinger operators on $\mathbb{Z}^d$: Uniform localization, J. Funct. Anal. 265 (2013), 435448 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) : 976989 .    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 KunzSouillard approach to localization in one dimension, J. Reine Angew. Math. 660 (2011), 99–130    David Damanik, Zheng Gan, Limitperiodic Schodinger operators with uniformly localized eigenfunctions, J. d'Analyse Math. 115 (2011), 33–49    David Damanik, Zheng Gan, Spectral properties of limitperiodic Schrodinger operators, Commun. Pure Appl. Anal. 10 (2011), 859871    David Damanik, Rowan Killip, Barry Simon, Perturbations of orthogonal polynomials with periodic recursion coeffcients, Ann. of Math. 171 (2010), 19312010    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), 13811412    David Damanik, Zheng Gan, Limitperiodic Schrodinger operators in the regime of positive Lyapunov exponents, J. Funct. Anal. 258 (2010), 40104025    Artur Avila, Jairo Bochi, David Damanik, Cantor spectrum for Schr\"odinger operators with potentials arising from generalized skewshifts, Duke Math. J. 146 (2009), 253280    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), 123143    David Damanik, Anton Gorodetski, The spectrum of the weakly coupled Fibonacci Hamiltonian, Electron. Res. Announc. Math. Sci. 16 (2009), 2329    David Damanik, G\"unter Stolz, A continuum version of the KunzSouillard 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), 813818    David Damanik, Jon Chaika, Helge Kr\"uger, Schr\"odinger operators defined by interval exchange transformations, J. Mod. Dyn. 3 (2009), 253270    David Damanik, Rafael del Rio, Quantum dynamical applications of Salem's theorem, Lett. Math. Phys. 89 (2009), 1319    David Damanik, Zheng Gan, Limitperiodic 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 noncritical coupling." Inventiones Mathematicae, 172 (2008) : 439453.    David Damanik, Alexander Pushnitski, Barry Simon "The analytic theory of matrix orthogonal polynomials." Surveys in Approximation Theory, 4 (2008) : 185.    David Damanik, Anton Gorodetski "The spectrum and the spectral type of the offdiagonal 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) : 16.    David Damanik, Mark Embree, Anton Gorodetski, Serguei Tcheremchantsev "The fractal dimension of the spectrum of the Fibonacci Hamiltonian." Communications in Mathematical Physics, 280 (2008) : 499516.    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 timeaveraging and tight lower bounds for the strongly coupled Fibonacci Hamiltonian." Journal of Functional Analysis, 255 (2008) : 28722887.    Michael Boshernitzan, David Damanik "Generic continuous spectrum for ergodic Schr\"odinger operators." Communications in Mathematical Physics, 283 (2008) : 647662.    Michael Boshernitzan, David Damanik "The repetition property for sequences on tori generated by polynomials or skewshifts." Isael Journal of MathematicsIn Press    David Damanik, Artur Avila "Absolute continiuty of the integrated density of states for the almost Mathieu operator with noncritical coupling." Invent. Math.In Press    David Damanik, Christian Remling "Schrödinger operators with many bound states." Duke Math. J., 136 (2007) : 5180.    David Damanik, Daniel Lenz "Uniform Szegö cocycles over strictly ergodic subshifts." J. Approx. Theory, 144 (2007) : 133138.    David Damanik, Gerald Teschl "Bound states of discrete Schrödinger operators with supercritical inverse square potentials." Proc. Amer. Math. Soc., 135 (2007) : 11231127.    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) : 221236.    David Damanik, Serguei Tcheremchantsev "Upper bounds in quantum dynamics." J. Amer. Math. Soc., 20 (2007) : 799827.    David Damanik "Verblunsky coefficients with Coulombtype decay." Journal of Approximation Theory, 139 (2006) : 257268.    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) : 150.    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) : 95123.    David Damanik, Daniel Lenz "Substitution dynamical systems: characterization of linear repetitivity and applications." Journal of Mathematical Analysis and Applications, 321 (2006) : 766780.    David Damanik, Daniel Lenz "Zeromeasure Cantor spectrum for Schrödinger operators with lowcomplexity potentials." Journal de Mathematiques Pures et Appliquees, 85 (2006) : 671686.    David Damanik, Daniel Lenz, Gunter Stolz "Lower transport bounds for onedimensional continuum Schrödinger operators." Mathematische Annalen, 336 (2006) : 361389.    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) : 307370.    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) : 539563.    David Damanik "Strictly ergodic subshifts and associated operators." Spectral theory and mathematical physics: a Festschrift in honor of Barry Simon's 60th birthday (2007) : 505538.    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 GeometryTopology Conference, Fort Worth. (02/20/16)    "Almost Periodicity in Time of Solutions of the KdV Equation." Mathematical Physics of Quasiperiodic 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 quasiperiodic Schrödinger operators I.." Mathematical Physics of Quasiperiodic Systems and Related Topics, Kyoto. (11/07/16)    "Some recent progress in the study of quasiperiodic Schrödinger operators II.." Mathematical Physics of Quasiperiodic Systems and Related Topics, Kyoto. (11/08/16)    "The spectrum of the continuum Fibonacci Hamiltonian." Spectral Theory of Periodic, Quasiperiodic, and Random Problems, London. (06/05/16)    Schr\"odinger spectrum and quantum dynamics, MiniWorkshop 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, AMSMeeting #1099$, Special Session on Hyperbolic Dynamics, Dynamically Defined Fractals, and Applications, University of New Mexico, Albuquerque, USA, April 5, 2014    Transport exponents associated with the Fibonacci Hamiltonian, AMSMeeting #1099$, 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, minicourse (series of nineteen 60minute lectures), Nanjing University, Nanjing, China, April 1026, 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 quasiperiodic 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
   Zeromeasure 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    AMSMeeting #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 ``NonUniform Hyperbolicity and Interval Exchange Maps,'' Program on ``Dynamics and PDE's, Institut MittagLeffler, Stockholm, Sweden. (April 7, 2010)    "Pseudorandomness 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 limitperiodic potentials." Forschungsseminar Analysis und Mathematische Physik, TU Chemnitz, Chemnitz, Germany. (June 16, 2010)    "Schrodinger operators with limitperiodic potentials." Oberseminar Geometrie, FriedrichSchillerUniversitat, 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 MittagLeffler, 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 1013, 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
KotaniLast 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 skewshift." Dynamical Systems Seminar, Northwestern University, Evanston. (October 28, 2008)    "Schr\"odinger cocycles over the skewshift." Dynamical Systems Seminar, University of Maryland, College Park. (November 6, 2008)    "Schr\"odinger cocycles over the skewshift." UNAM, Mexico City. (November 24. 2008)    "Schr\"odinger operators with dynamically defined
potentials." Mathematics Colloquium, PUCRio, Rio de Janeiro. (August 6, 2008)    "Schr\"odinger operators with potentials generated by
lowcomplexity dynamical systems." Workshop on Low Complexity Dynamics, BIRS, Banff. (May 29, 2008)    "Schr\"odinger operators with potentials generated by
the skewshift." 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 skewshift model and pseudorandomness 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 75minute lectures), Universit\"at Bielefeld, Bielefeld. (June 11July 4, 2008)    "Hyperbolicity, fractal dimension, and quantum
dynamics for the Fibonacci Hamiltonian." Workshop on ``Transport in MultiDimensional 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 quasiperiodic operators." ICMP 2006, Rio de Janeiro. (7 Aug 2006)    Keynote Speaker   Invited onehour 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)    "Nonuniformly hyperbolic Schrodinger equations." NonUniformly Hyperbolic Days, Pontificia Universidad Cat\'olica de Chile, Santiago, Chile. (January 18, 2010)    Lectures   Cantor sets and Cantor measures, Oberseminar Geometrie, FriedrichSchillerUniversit\"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 minicourse with Anton Gorodetski (series of four 60minute lectures), Workshop on ``Dynamical Methods in the Spectral Theory of Quasicrystals,'' University of California, Irvine, USA, May 1619, 2013    Mathematics Colloquium, Williams College, Williamstown, USA, May 6, 2011    MiniCourse (series of five 60minute 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." RuhrUniversitaet, 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." FriedrichAlexanderUniversitaet, ErlangenNuernberg, 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)    "Almostperiodic 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 KunzSouillard 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 LiebRobinson bounds, Arbeitsgemeinschaft Mathematische Physik, FriedrichAlexanderUniversit\"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, LudwigMaximiliansUniversitat, Munich, Germany, July 5, 2011    Arbeitsgemeinschaft Mathematische Physik, FriedrichAlexanderUniversitat, 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 limitperiodic Schr\"odinger operators." Mathematics in the Natural Sciences Seminar, Universit\"at Bielefeld, Bielefeld, Germany. (May 22, 2009)    "Cantor groups and limitperiodic Schr\"odinger operators." Mathematical Physics Seminar, LudwigMaximiliansUniversit\"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." LudwigMaximiliansUniversitaet, 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, minicourse (series of four 60minute lectures), ``Periodic, AlmostPeriodic, and Random Operators: Instructional School,'' Isaac Newton Institute for Mathematical Sciences, Cambridge, UK." (January 57, 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 quasiperiodic Schr\"odinger operators and applications, AMSMeeting #1114, Special Session on ``Spectral Theory of Ergodic Schr\"odinger Operators and Related Models,'' California State University, Fullerton, USA." (October 24, 2015)    MiniWorkshop 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 Odiagonal Fibonacci Operator. (2011) (Thesis Director)
  Zheng Gan, Ph.D. Spectral Properties of LimitPeriodic Schrodinger Operators. (2012) (Thesis Director)
  Zheng Gan, Ph. D. LimitPeriodic 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 OneDimensional 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)

