E-mail: (first name).(last name) at rice.edu |

Since July 2014, I am a postdoctoral fellow at University of Toronto. My new web page is http://www.math.toronto.edu/mlukic/

- 2014- Postdoctoral Fellow, University of Toronto
- 2011-2014 Evans Instructor, Rice University

- Ph.D., Mathematics, California Institute of Technology, Pasadena, CA, 2011 [Thesis]
- M.Sc., Physics, California Institute of Technology, Pasadena, CA, 2010
- B.Sc., Astrophysics, University of Belgrade, Belgrade, Serbia, 2007
- B.Sc., Mathematics, University of Belgrade, Belgrade, Serbia, 2006

My main area of research is the spectral theory of self-adjoint and unitary operators, especially Schrodinger, Jacobi, and CMV operators, but also Hamiltonians in spin systems. More broadly, I am interested in analysis and mathematical physics.

My research is partially supported by NSF Grant DMS-1301582.

- (with J. Fillman) Spectral Homogeneity of Limit-Periodic Schrödinger Operators, submitted [arXiv:1502.05454]
- (with D. C. Ong) Generalized Prüfer variables for perturbations of Jacobi and CMV matrices, submitted [arXiv:1409.7116]
- (with D. Damanik, J. Fillman, W. Yessen) Characterizations of Uniform Hyperbolicity and Spectra of CMV Matrices, Discrete Contin. Dyn. Syst. Ser. S, to appear [arXiv:1409.6259]
- (with D. Damanik, M. Goldstein) The Isospectral Torus of Quasi-Periodic Schrödinger Operators via Periodic Approximations, submitted [arXiv:1409.2434]
- (with D. Damanik, M. Goldstein) A Multi-Scale Analysis Scheme on Abelian Groups with an Application to Operators Dual to Hill's Equation, Trans. Amer. Math. Soc., to appear [arXiv:1409.2147]
- (with D. Damanik, M. Goldstein) The Spectrum of a Schrödinger Operator With Small Quasi-Periodic Potential is Homogeneous, J. Spectr. Theory, to appear [arXiv:1408.4335]
- (with D. Damanik, M. Lemm, W. Yessen) New Anomalous Lieb-Robinson Bounds in Quasi-Periodic XY Chains, Phys. Rev. Lett., 113 (2014), 127202 [journal] [arXiv:1408.1796]
- (with D. Damanik, M. Lemm, W. Yessen) On Anomalous Lieb-Robinson Bounds for the Fibonacci XY Chain, J. Spectr. Theory, to appear [arXiv:1407.4924]
- (with D. Damanik, W. Yessen) Quantum Dynamics of Periodic and Limit-Periodic Jacobi and Block Jacobi Matrices with Applications to Some Quantum Many Body Problems, Comm. Math. Phys., 337 (2015), 1535-1561 [journal] [arXiv:1407.5067]
- (with D. Damanik, J. Fillman, W. Yessen) Uniform Hyperbolicity for Szegő Cocycles and Applications to Random CMV Matrices and the Ising Model, Int. Math. Res. Not., to appear [journal] [arXiv:1404.7065]
- (with M. Boshernitzan, D. Damanik, J. Fillman) Ergodic Schrödinger operators in the infinite measure setting, in preparation
- On higher-order Szegő theorems with a single critical point of arbitrary order, submitted [arXiv:1310.6712]
- (with Y. Last) Square-summable q-variations and absolutely continuous spectrum of Jacobi matrices, in preparation
- (with D. C. Ong) Wigner-von Neumann type perturbations of periodic Schrödinger operators, Trans. Amer. Math. Soc. 367 (2015), 707-724 [journal] [arXiv:1305.6124]
- Square-summable variation and absolutely continuous spectrum, J. Spectr. Theory 4 (2014), 815-840 [journal] [arXiv:1303.4161]
- On a conjecture for higher-order Szegő theorems, Constr. Approx. 38 (2013), 161-169 [journal] [arXiv:1210.6953]
- A class of Schrödinger operators with decaying oscillatory potentials, Comm. Math. Phys. 326 (2014), 441-458 [journal] [arXiv:1207.5077]
- Schrödinger operators with slowly decaying Wigner-von Neumann type potentials, J. Spectr. Theory 3 (2013), 147-169 [journal] [arXiv:1201.4840]
- Derivatives of L^p eigenfunctions of Schrödinger operators, Math. Model. Nat. Phenom. 8 (2013), 170-174 [journal] [arXiv:1112.3673]
- Jacobi and CMV matrices with coefficients of generalized bounded variation, Operator Theory: Advances and Applications 227 (2013), 117-121
- Orthogonal polynomials with recursion coefficients of generalized bounded variation, Comm. Math. Phys. 306 (2011), 485-509 [journal] [arXiv:1008.3844]

- MATH 322: Introduction to Analysis II (Spring 2014)
- MATH 211, Section 1: Ordinary Differential Equations and Linear Algebra (Spring 2014)
- MATH 428/518: Topics in Complex Analysis (Fall 2013)
- MATH 102, Section 3: Single Variable Calculus II (Spring 2013)
- MATH 370: Calculus on Manifolds (Spring 2013)
- MATH 211, Section 2: Ordinary Differential Equations and Linear Algebra (Fall 2012)
- MATH 212, Section 4: Multivariable Calculus (Spring 2012)
- MATH 381: Introduction to Partial Differential Equations (Fall 2011)
- MATH 211, Section 5: Ordinary Differential Equations and Linear Algebra (Fall 2011)