## Milivoje Lukic

Assistant Professor

Department of Mathematics
Rice University

Office:  HBH 418

E-mail:  milivoje.lukic at rice.edu

#### Employment

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

#### Degrees

• Ph.D., Mathematics, California Institute of Technology, Pasadena, CA, 2011
• M.Sc., Physics, California Institute of Technology, Pasadena, CA, 2010

#### 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.

#### Research articles

1. Spectral edge behavior for eventually monotone Jacobi and Verblunsky coefficients
preprint [arXiv]
2. (with Y. Last) $$\ell^2$$ bounded variation and absolutely continuous spectrum of Jacobi matrices
Comm. Math. Phys., to appear [arXiv]
3. (with I. Binder, D. Damanik, T. VandenBoom) Almost Periodicity in Time of Solutions of the Toda Lattice
preprint [arXiv]
4. (with I. Binder, D. Damanik, M. Goldstein) Almost Periodicity in Time of Solutions of the KdV Equation
submitted [arXiv]
5. (with D. Damanik, J. Fillman) Limit-Periodic Continuum Schrödinger Operators with Zero Measure Cantor Spectrum
J. Spectr. Theory, to appear [arXiv]
6. (with J. Fillman) Spectral Homogeneity of Limit-Periodic Schrödinger Operators
J. Spectr. Theory 7 (2017), 387-406 [journal] [arXiv]
7. (with D. C. Ong) Generalized Prüfer variables for perturbations of Jacobi and CMV matrices
J. Math. Anal. Appl. 444 (2016), 1490-1514 [journal] [arXiv]
8. (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]
9. (with D. Damanik, M. Goldstein) The Isospectral Torus of Quasi-Periodic Schrödinger Operators via Periodic Approximations
Invent. Math. 207 (2017), 895-980 [journal] [arXiv]
10. (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]
11. (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]
12. (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]
13. (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]
14. (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]
15. (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]
16. On higher-order Szegő theorems with a single critical point of arbitrary order
Constr. Approx. 44 (2016), 283-296 [journal] [arXiv]
17. (with D. C. Ong) Wigner-von Neumann type perturbations of periodic Schrödinger operators
Trans. Amer. Math. Soc. 367 (2015), 707-724 [journal] [arXiv]
18. Square-summable variation and absolutely continuous spectrum
J. Spectr. Theory 4 (2014), 815-840 [journal] [arXiv]
19. On a conjecture for higher-order Szegő theorems
Constr. Approx. 38 (2013), 161-169 [journal] [arXiv]
20. A class of Schrödinger operators with decaying oscillatory potentials
Comm. Math. Phys. 326 (2014), 441-458 [journal] [arXiv]
21. Schrödinger operators with slowly decaying Wigner-von Neumann type potentials
J. Spectr. Theory 3 (2013), 147-169 [journal] [arXiv]
22. Derivatives of L^p eigenfunctions of Schrödinger operators
Math. Model. Nat. Phenom. 8 (2013), 170-174 [journal] [arXiv]
23. 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. Djukic, I. Matic) Inequalities
(in Serbian, math olympiad training textbook) Mathematical Society of Serbia (2003)

#### Current teaching (Fall 2017)

• MATH 102, Section 3: Single Variable Calculus II
• MATH 425/515: Integration Theory

#### Past teaching at Rice University (2016-)

• MATH 212, Section 1: Multivariable Calculus (Fall 2016)
• MATH 300: Topics in Undergraduate Math (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)