Milivoje Lukic

Milivoje Lukić

Associate Professor

Department of Mathematics
Rice University

Office:  HBH 418

E-mail:  milivoje.lukic at



Research Interests

Analysis and mathematical physics. In particular: direct and inverse spectral theory of Schrödinger operators; spin systems; KdV equation and other nonlinear "integrable" partial differential equations.

My research is partially supported by NSF Grant DMS-1700179; previously supported by DMS-1301582.

Profile on MathSciNet     List of papers on arXiv

Research articles

  1. (with B. Eichinger, G. Young)
    Orthogonal rational functions with real poles, root asymptotics, and GMP matrices
    preprint [arXiv]
  2. (with B. Eichinger)
    Stahl-Totik regularity for continuum Schrödinger operators
    submitted [arXiv]
  3. (with G. Young)
    Uniqueness of solutions of the KdV-hierarchy via Dubrovin-type flows
    J. Funct. Anal. [journal] [arXiv]
  4. (with M. Boshernitzan, D. Damanik, J. Fillman)
    Ergodic Schrödinger Operators in the Infinite Measure Setting
    J. Spectr. Theory, to appear [arXiv]
  5. Spectral edge behavior for eventually monotone Jacobi and Verblunsky coefficients
    J. Spectr. Theory 9 (2019), 1115-1155 [journal] [arXiv]
  6. (with Y. Last)
    \(\ell^2\) bounded variation and absolutely continuous spectrum of Jacobi matrices
    Comm. Math. Phys. 359 (2018), 101-119 [journal] [arXiv]
  7. (with I. Binder, D. Damanik, T. VandenBoom)
    Almost Periodicity in Time of Solutions of the Toda Lattice
    C. R. Math. Rep. Acad. Sci. Canada 40 (2018), 1-28 [journal] [arXiv]
  8. (with I. Binder, D. Damanik, M. Goldstein)
    Almost Periodicity in Time of Solutions of the KdV Equation
    Duke Math. J. 167 (2018), 2633-2678 [journal] [arXiv]
  9. (with D. Damanik, J. Fillman)
    Limit-Periodic Continuum Schrödinger Operators with Zero Measure Cantor Spectrum
    J. Spectr. Theory 7 (2017), 1101-1118 [journal] [arXiv]
  10. (with J. Fillman)
    Spectral Homogeneity of Limit-Periodic Schrödinger Operators
    J. Spectr. Theory 7 (2017), 387-406 [journal] [arXiv]
  11. (with D. C. Ong)
    Generalized Prüfer variables for perturbations of Jacobi and CMV matrices
    J. Math. Anal. Appl. 444 (2016), 1490-1514 [journal] [arXiv]
  12. (with D. Damanik, J. Fillman, W. Yessen)
    Characterizations of Uniform Hyperbolicity and Spectra of CMV Matrices
    Discrete Contin. Dyn. Syst. Ser. S 9 (2016), 1009-1023 [journal] [arXiv]
  13. (with D. Damanik, M. Goldstein)
    The Isospectral Torus of Quasi-Periodic Schrödinger Operators via Periodic Approximations
    Invent. Math. 207 (2017), 895-980 [journal] [arXiv]
  14. (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. 369 (2017), 1689-1755 [journal] [arXiv]
  15. (with D. Damanik, M. Goldstein)
    The Spectrum of a Schrödinger Operator With Small Quasi-Periodic Potential is Homogeneous
    J. Spectr. Theory 6 (2016), 415-427 [journal] [arXiv]
  16. (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]
  17. (with D. Damanik, M. Lemm, W. Yessen)
    On Anomalous Lieb-Robinson Bounds for the Fibonacci XY Chain
    J. Spectr. Theory 6 (2016), 601-628 [journal] [arXiv]
  18. (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]
  19. (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. 2015 (2015), 7110-7129 [journal] [arXiv]
  20. On higher-order Szegő theorems with a single critical point of arbitrary order
    Constr. Approx. 44 (2016), 283-296 [journal] [arXiv]
  21. (with D. C. Ong)
    Wigner-von Neumann type perturbations of periodic Schrödinger operators
    Trans. Amer. Math. Soc. 367 (2015), 707-724 [journal] [arXiv]
  22. Square-summable variation and absolutely continuous spectrum
    J. Spectr. Theory 4 (2014), 815-840 [journal] [arXiv]
  23. On a conjecture for higher-order Szegő theorems
    Constr. Approx. 38 (2013), 161-169 [journal] [arXiv]
  24. A class of Schrödinger operators with decaying oscillatory potentials
    Comm. Math. Phys. 326 (2014), 441-458 [journal] [arXiv]
  25. Schrödinger operators with slowly decaying Wigner-von Neumann type potentials
    J. Spectr. Theory 3 (2013), 147-169 [journal] [arXiv]
  26. Derivatives of L^p eigenfunctions of Schrödinger operators
    Math. Model. Nat. Phenom. 8 (2013), 170-174 [journal] [arXiv]
  27. Orthogonal polynomials with recursion coefficients of generalized bounded variation
    Comm. Math. Phys. 306 (2011), 485-509 [journal] [arXiv]

Other publications

  1. Jacobi and CMV matrices with coefficients of generalized bounded variation
    Operator Theory: Advances and Applications 227 (2013), 117-121
  2. Spectral theory for generalized bounded variation perturbations of orthogonal polynomials and Schrödinger operators
    Ph.D. Dissertation, California Institute of Technology (2011) [thesis]
  3. (with Z. Kadelburg, D. Djukić, I. Matić) Inequalities
    (in Serbian, math olympiad training textbook) Mathematical Society of Serbia (2003)

Current teaching (Fall 2020): None

Past teaching at Rice University (2016-)

  • MATH 425/515: Integration Theory (Fall 2019)
  • MATH 321: Introduction to Analysis (Fall 2019)
  • MATH 522: Topics in Analysis: Schrödinger operators and the KdV equation (Spring 2019)
  • MATH 222: Honors Calculus IV (Spring 2019)
  • MATH 425/515: Integration Theory (Fall 2017)
  • MATH 102, Section 3: Single Variable Calculus II (Fall 2017)
  • MATH 300: Topics in Undergraduate Math (Fall 2016)
  • MATH 212, Section 1: Multivariable Calculus (Fall 2016)

Past teaching at University of Toronto (2014-2016)

  • MAT236H5: Vector Calculus (Winter 2016)
  • MAT223H5: Linear Algebra I (Fall 2015)
  • MAT212H5: Modeling with Differential Equations in Life Sciences and Medicine (Fall 2014)
  • MAT223H5: Linear Algebra I (Fall 2014)

Past teaching at Rice University (2011-2014)

  • 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)