Associate Professor

Department of Mathematics

Rice University

Office: HBH 418

E-mail: milivoje.lukic at rice.edu

- 2018- Associate Professor, Rice University
- 2016-2018 Assistant Professor, Rice University
- 2014-2016 Postdoctoral Fellow, University of Toronto
- 2011-2014 Evans Instructor, Rice University

- Ph.D., Mathematics, California Institute of Technology, Pasadena, CA, 2011
- 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

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.

- (with B. Eichinger, G. Young)

Orthogonal rational functions with real poles, root asymptotics, and GMP matrices

preprint [arXiv] - (with B. Eichinger)

Stahl-Totik regularity for continuum Schrödinger operators

submitted [arXiv] - (with G. Young)

Uniqueness of solutions of the KdV-hierarchy via Dubrovin-type flows

J. Funct. Anal. [journal] [arXiv] - (with M. Boshernitzan, D. Damanik, J. Fillman)

Ergodic Schrödinger Operators in the Infinite Measure Setting

J. Spectr. Theory, to appear [arXiv] - Spectral edge behavior for eventually monotone Jacobi and Verblunsky coefficients

J. Spectr. Theory 9 (2019), 1115-1155 [journal] [arXiv] - (with Y. Last)

\(\ell^2\) bounded variation and absolutely continuous spectrum of Jacobi matrices

Comm. Math. Phys. 359 (2018), 101-119 [journal] [arXiv] - (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] - (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] - (with D. Damanik, J. Fillman)

Limit-Periodic Continuum Schrödinger Operators with Zero Measure Cantor Spectrum

J. Spectr. Theory 7 (2017), 1101-1118 [journal] [arXiv] - (with J. Fillman)

Spectral Homogeneity of Limit-Periodic Schrödinger Operators

J. Spectr. Theory 7 (2017), 387-406 [journal] [arXiv] - (with D. C. Ong)

Generalized Prüfer variables for perturbations of Jacobi and CMV matrices

J. Math. Anal. Appl. 444 (2016), 1490-1514 [journal] [arXiv] - (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] - (with D. Damanik, M. Goldstein)

The Isospectral Torus of Quasi-Periodic Schrödinger Operators via Periodic Approximations

Invent. Math. 207 (2017), 895-980 [journal] [arXiv] - (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] - (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] - (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] - (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] - (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] - (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] - On higher-order Szegő theorems with a single critical point of arbitrary order

Constr. Approx. 44 (2016), 283-296 [journal] [arXiv] - (with D. C. Ong)

Wigner-von Neumann type perturbations of periodic Schrödinger operators

Trans. Amer. Math. Soc. 367 (2015), 707-724 [journal] [arXiv] - Square-summable variation and absolutely continuous spectrum

J. Spectr. Theory 4 (2014), 815-840 [journal] [arXiv] - On a conjecture for higher-order Szegő theorems

Constr. Approx. 38 (2013), 161-169 [journal] [arXiv] - A class of Schrödinger operators with decaying oscillatory potentials

Comm. Math. Phys. 326 (2014), 441-458 [journal] [arXiv] - Schrödinger operators with slowly decaying Wigner-von Neumann type potentials

J. Spectr. Theory 3 (2013), 147-169 [journal] [arXiv] - Derivatives of L^p eigenfunctions of Schrödinger operators

Math. Model. Nat. Phenom. 8 (2013), 170-174 [journal] [arXiv] - Orthogonal polynomials with recursion coefficients of generalized bounded variation

Comm. Math. Phys. 306 (2011), 485-509 [journal] [arXiv]

- Jacobi and CMV matrices with coefficients of generalized bounded variation

Operator Theory: Advances and Applications 227 (2013), 117-121 - Spectral theory for generalized bounded variation perturbations of orthogonal polynomials and Schrödinger operators

Ph.D. Dissertation, California Institute of Technology (2011) [thesis] - (with Z. Kadelburg, D. Djukić, I. Matić) Inequalities

(in Serbian, math olympiad training textbook) Mathematical Society of Serbia (2003)

- 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)

- 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)

- 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)