Employment

• 2023-         Professor, Rice University
• 2018-2023 Associate Professor, Rice University
• 2016-2018 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
• B.Sc., Astrophysics, University of Belgrade, Belgrade, Serbia, 2007
• B.Sc., Mathematics, University of Belgrade, Belgrade, Serbia, 2006

Research interests

Analysis and mathematical physics. In particular:

• direct and inverse spectral theory of Schrödinger operators and canonical systems
• connections between spectral theory and potential theory and harmonic analysis
• KdV, NLS, and other nonlinear integrable partial differential equations
• universality phenomena in orthogonal polynomials and random matrices

I am an editor for the Journal of Spectral Theory and for the New York Journal of Mathematics.

I co-organize the Analysis Seminar at Rice University.

Research articles

1. Necessary and sufficient conditions for universality limits (with B. Eichinger, H. Woracek)
   [arXiv:2409.18045]
2. On point spectrum of Jacobi matrices generated by iterations of quadratic polynomials (with B. Eichinger, P. Yuditskii)
   [arXiv:2405.19470]
3. Modified Jost solutions of Schrödinger operators with locally \(H^{-1}\) potentials (with X. Wang)
   [arXiv:2405.17715]
4. Spectral properties of Schrödinger operators with locally \(H^{-1}\) potentials (with S. Sukhtaiev, X. Wang)
   J. Spectr. Theory 14 (2024), 59-120 [arXiv:2206.07079]
5. Limit-Periodic Dirac Operators with Thin Spectra (with B. Eichinger, J. Fillman, E. Gwaltney)
   J. Funct. Anal. 283 (2022), 109711 [arXiv]
6. The Deift Conjecture: A Program to Construct a Counterexample (with D. Damanik, A. Volberg, P. Yuditskii)
   [arXiv:2111.09345]
7. An approach to universality using Weyl m-functions (with B. Eichinger, B. Simanek)
   [arXiv:2108.01629]
8. Asymptotics of Chebyshev rational functions with respect to subsets of the real line (with B. Eichinger, G. Young)
   Constr. Approx. 59, 541-581 (2024) [arXiv]
9. Stahl-Totik regularity for Dirac operators (with B. Eichinger, E. Gwaltney)
   [arXiv:2012.12889]
10. Reflectionless canonical systems, II. Almost periodicity and character-automorphic Fourier transforms (with R. Bessonov, P. Yuditskii)
    Adv. Math. 444 (2024), Paper No. 109636. [arXiv]
11. Reflectionless canonical systems, I. Arov gauge and right limits (with R. Bessonov, P. Yuditskii)
    Integr. Equ. Oper. Theory 94 (2022), 4 [arXiv]
12. Orthogonal rational functions with real poles, root asymptotics, and GMP matrices (with B. Eichinger, G. Young)
    Trans. Amer. Math. Soc. Ser. B 10 (2023), 1-47 [arXiv]
13. Stahl-Totik regularity for continuum Schrödinger operators (with B. Eichinger)
    Anal. PDE , accepted [arXiv:2001.00875]
14. Uniqueness of solutions of the KdV-hierarchy via Dubrovin-type flows (with G. Young)
    J. Funct. Anal. 279 (2020), 108705 [arXiv]
15. Ergodic Schrödinger Operators in the Infinite Measure Setting (with M. Boshernitzan, D. Damanik, J. Fillman)
    J. Spectr. Theory 11 (2021), 873-902 [arXiv]
16. Spectral edge behavior for eventually monotone Jacobi and Verblunsky coefficients
    J. Spectr. Theory 9 (2019), 1115-1155 [arXiv]
17. \(\ell^2\) bounded variation and absolutely continuous spectrum of Jacobi matrices (with Y. Last)
    Comm. Math. Phys. 359 (2018), 101-119 [arXiv]
18. Almost Periodicity in Time of Solutions of the Toda Lattice (with I. Binder, D. Damanik, T. VandenBoom)
    C. R. Math. Rep. Acad. Sci. Canada 40 (2018), 1-28 [arXiv]
19. Almost Periodicity in Time of Solutions of the KdV Equation (with I. Binder, D. Damanik, M. Goldstein)
    Duke Math. J. 167 (2018), 2633-2678 [arXiv]
20. Limit-Periodic Continuum Schrödinger Operators with Zero Measure Cantor Spectrum (with D. Damanik, J. Fillman)
    J. Spectr. Theory 7 (2017), 1101-1118 [arXiv]
21. Spectral Homogeneity of Limit-Periodic Schrödinger Operators (with J. Fillman)
    J. Spectr. Theory 7 (2017), 387-406 [arXiv]
22. Generalized Prüfer variables for perturbations of Jacobi and CMV matrices (with D. C. Ong)
    J. Math. Anal. Appl. 444 (2016), 1490-1514 [arXiv]
23. Characterizations of Uniform Hyperbolicity and Spectra of CMV Matrices (with D. Damanik, J. Fillman, W. Yessen)
    Discrete Contin. Dyn. Syst. Ser. S 9 (2016), 1009-1023 [arXiv]
24. The Isospectral Torus of Quasi-Periodic Schrödinger Operators via Periodic Approximations (with D. Damanik, M. Goldstein)
    Invent. Math. 207 (2017), 895-980 [arXiv]
25. A Multi-Scale Analysis Scheme on Abelian Groups with an Application to Operators Dual to Hill's Equation (with D. Damanik, M. Goldstein)
    Trans. Amer. Math. Soc. 369 (2017), 1689-1755 [arXiv]
26. The Spectrum of a Schrödinger Operator With Small Quasi-Periodic Potential is Homogeneous (with D. Damanik, M. Goldstein)
    J. Spectr. Theory 6 (2016), 415-427 [arXiv]
27. New Anomalous Lieb-Robinson Bounds in Quasi-Periodic XY Chains (with D. Damanik, M. Lemm, W. Yessen)
    Phys. Rev. Lett. 113 (2014), 127202 [arXiv]
28. On Anomalous Lieb-Robinson Bounds for the Fibonacci XY Chain (with D. Damanik, M. Lemm, W. Yessen)
    J. Spectr. Theory 6 (2016), 601-628 [arXiv]
29. Quantum Dynamics of Periodic and Limit-Periodic Jacobi and Block Jacobi Matrices with Applications to Some Quantum Many Body Problems (with D. Damanik, W. Yessen)
    Comm. Math. Phys. 337 (2015), 1535-1561 [arXiv]
30. Uniform Hyperbolicity for Szegő Cocycles and Applications to Random CMV Matrices and the Ising Model (with D. Damanik, J. Fillman, W. Yessen)
    Int. Math. Res. Not. 2015 (2015), 7110-7129 [arXiv]
31. On higher-order Szegő theorems with a single critical point of arbitrary order
    Constr. Approx. 44 (2016), 283-296 [arXiv]
32. Wigner-von Neumann type perturbations of periodic Schrödinger operators (with D. C. Ong)
    Trans. Amer. Math. Soc. 367 (2015), 707-724 [arXiv]
33. Square-summable variation and absolutely continuous spectrum
    J. Spectr. Theory 4 (2014), 815-840 [arXiv]
34. On a conjecture for higher-order Szegő theorems
    Constr. Approx. 38 (2013), 161-169 [arXiv]
35. A class of Schrödinger operators with decaying oscillatory potentials
    Comm. Math. Phys. 326 (2014), 441-458 [arXiv]
36. Schrödinger operators with slowly decaying Wigner-von Neumann type potentials
    J. Spectr. Theory 3 (2013), 147-169 [arXiv]
37. Derivatives of \(L^p\) eigenfunctions of Schrödinger operators
    Math. Model. Nat. Phenom. 8 (2013), 170-174 [arXiv]
38. Orthogonal polynomials with recursion coefficients of generalized bounded variation
    Comm. Math. Phys. 306 (2011), 485-509 [arXiv]

Other publications

1. A first course in spectral theory
   Graduate Studies in Mathematics, 226. American Mathematical Society, Providence, RI, 2022. xvi+472 pp.
2. Jacobi and CMV matrices with coefficients of generalized bounded variation
   Operator Theory: Advances and Applications 227 (2013), 117-121
3. Spectral theory for generalized bounded variation perturbations of orthogonal polynomials and Schrödinger operators
   Ph.D. Dissertation, California Institute of Technology (2011)
4. Inequalities of Karamata, Schur and Muirhead, and some applications (with Z. Kadelburg, D. Djukić, I. Matić)
   The Teaching of Mathematics 8 (2005), pp. 31-45
5. Inequalities (with Z. Kadelburg, D. Djukić, I. Matić)
   (in Serbian, math olympiad training textbook, 212 pages) Mathematical Society of Serbia (2003)

Upcoming teaching (Fall 2024)

• MATH 412: Probability Theory
• MATH 522: Topics in Analysis