ACADEMIC PUBLICATIONS

ALMOST EVERYTHING ABOUT THE UNITARY ALMOST MATHIEU OPERATOR (WITH C. CEDZICH AND J. FILLMAN)

https://arxiv.org/abs/2112.03216

SIMON'S OPUC HAUSDORFF DIMENSION CONJECTURE
(WITH D. DAMANIK AND S. GUO)

Mathematische Annalen, 384, 1-37 (2022)

SUBORDINACY THEORY FOR EXTENDED CMV MATRICES
(WITH S. GUO AND D. DAMANIK)

Science China Mathematics 65,  539–558 (2022)

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ON SIMON’S HAUSDORFF DIMENSION CONJECTURE
(WITH D. DAMANIK, J. FILLMAN, AND S. GUO)

In: Gesztesy F., Martinez-Finkelshtein A. (eds) From Operator Theory to Orthogonal Polynomials, Combinatorics, and Number Theory. Operator Theory: Advances and Applications, vol 285. Birkhäuser, Cham.

RESTRICTIONS ON THE EXISTENCE OF A CANONICAL SYSTEM FLOW HIERARCHY

(WITH I. HUR)

Integral Equations and Operator Theory 93, Number 40 (2021)

QUASIPERIODIC MUSIC

Journal of Mathematics and the Arts, 14, Issue 4, 285-296 (2020)

SHARP SPECTRAL TRANSITION FOR EIGENVALUES EMBEDDED INTO THE SPECTRAL BANDS OF PERTURBED PERIODIC OPERATORS
(WITH W. LIU)

Journal d’Analyse Mathematique 141, 625–661 (2020)

GENERALIZED TODA FLOWS 

(WITH C. REMLING)

Transactions of the American Mathematical Society 371, Issue 7, 5069–5081 (2019)

SPECTRAL APPROXIMATION FOR ERGODIC CMV OPERATORS WITH AN APPLICATION TO QUANTUM WALKS 

(WITH J.FILLMAN AND T. VANDENBOOM)

Journal of Mathematical Analysis and Applications, 467, Issue 1, 132-147 (2018)

ON A DESCRIPTION OF THE TODA HIERARCHY USING COCYCLE MAPS

Linear Algebra and its Applications 549, 12-29 (2018)

A CONDITION FOR PURELY ABSOLUTELY CONTINUOUS SPECTRUM FOR CMV OPERATORS USING THE DENSITY OF STATES 

(WITH J. FILLMAN)

Proceedings of the American Mathematical Society 146, Issue 2, 571-580 (2018)

PURELY SINGULAR CONTINUOUS SPECTRUM FOR LIMIT-PERIODIC CMV OPERATORS WITH APPLICATIONS TO QUANTUM WALKS 

(WITH J. FILLMAN).

Journal of Functional Analysis 272, Issue 12, 5107-5143 (2017)

SPECTRAL CHARACTERISTICS OF THE UNITARY CRITICAL ALMOST-MATHIEU OPERATOR 

(WITH J. FILLMAN AND Z. ZHANG)

Communications in Mathematical Physics 351, Issue 2, 525-561 (2017)

GENERALIZED PRÜFER VARIABLES FOR PERTURBATIONS OF JACOBI AND CMV MATRICES 

(WITH M. LUKIC)

 Journal of Mathematical Analysis and Applications, 444, Issue 2, 1490-1514 (2016)

SPREADING ESTIMATES FOR QUANTUM WALKS ON THE INTEGER LATTICE VIA POWER-LAW BOUNDS ON TRANSFER MATRICES 

(WITH D. DAMANIK AND J. FILLMAN)

Journal de Mathématiques Pures et Appliquées, 105, Issue 3, 293-341 (2016)

WIGNER-VON NEUMANN TYPE PERTURBATIONS OF PERIODIC SCHRÖDINGER OPERATORS 

(WITH M. LUKIC)

 Transactions of the American Mathematical Society 367, 707-724 (2015)

HÖLDER CONTINUITY OF SPECTRAL MEASURES OF AN EXTENDED CMV MATRIX 

(WITH P. MUNGER)

Journal of Mathematical Physics 55, 093507 (2014)

PURELY SINGULAR CONTINUOUS SPECTRUM FOR CMV OPERATORS GENERATED BY SUBSHIFTS

Journal of Statistical Physics 155, 763-776 (2014)

ORTHOGONAL POLYNOMIALS ON THE UNIT CIRCLE WITH QUASIPERIODIC VERBLUNSKY COEFFICIENTS HAVE GENERIC PURELY SINGULAR CONTINUOUS SPECTRUM

Discrete and Continuous Dynamical Systems. Proceedings of the 9th AIMS Conference Special Issue, pp. 605-609 (2013)

LIMIT-PERIODIC VERBLUNSKY COEFFICIENTS FOR ORTHOGONAL POLYNOMIALS ON THE UNIT CIRCLE

Journal of Mathematical Analysis and Applications 394.2, 633-644 (2012)

ON A THEOREM OF INTERSECTING CONICS

Forum Geometricorum 11, 95-107 (2011).

THE FROBENIUS NUMBER OF GEOMETRIC SEQUENCES 

(WITH V.PONOMARENKO)

INTEGERS: The Electronic Journal of Combinatorial Number Theory 8, A33 (2008)