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Scholarly Interest Report
         
Milivoje Lukic
Assistant Professor
Assistant Professor of Mathematics
 
e-mail:Milivoje.Lukic@rice.edu
 
  • Ph.D. Mathematics (2011) California Institute of Technology, Pasadena, CA
  • M.Sc. Physics (2010) California Institute of Technology, Pasadena, CA
  • B.Sc. Astrophysics (2007) University of Belgrade, Belgrade, Serbia
  • B.Sc. Mathematics (2006) University of Belgrade, Belgrade, Serbia
 
Primary Department
   Department of Mathematics
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Websites
 webpage
 
Research Areas
 Schrodinger operators, orthogonal polynomials
 
Selected Publications
 Refereed articles
 

D. Damanik, J. Fillman, M. Lukic, W. Yessen "Characterizations of Uniform Hyperbolicity and Spectra of CMV Matrices." Discrete and Continuous Dynamical Systems - Series S, 9 (2016) : 1009-1023.

 
 

D. Damanik, M. Goldstein, M. Lukic "A Multi-Scale Analysis Scheme on Abelian Groups with an Application to Operators Dual to Hill's Equation." Transactions of the American Mathematical Society, 369 (2017) : 1689-1755.In Press

 
 

D. Damanik, M. Goldstein, M. Lukic "The Isospectral Torus of Quasi-Periodic Schrödinger Operators via Periodic Approximations." Inventiones Mathematicae, 207 (2017) : 895-980.In Press

 
 

D. Damanik, M. Goldstein, M. Lukic "The Spectrum of a Schrödinger Operator With Small Quasi-Periodic Potential is Homogeneous." Journal of Spectral Theory, 6 (2016) : 415-427.

 
 

D. Damanik, M. Lemm, M. Lukic, W. Yessen "On Anomalous Lieb-Robinson Bounds for the Fibonacci XY Chain." Journal of Spectral Theory, 6 (2016) : 601-628.

 
 

M. Lukic "On higher-order Szegő theorems with a single critical point of arbitrary order." Constructive Approximation, 44 (2016) : 283-296.

 
 

M. Lukic, D. C. Ong "Generalized Prüfer variables for perturbations of Jacobi and CMV matrices." Journal of Mathematical Analysis and Applications, 444 (2016) : 1490-1514.

 
 

Milivoje Lukic "A class of Schrödinger operators with decaying oscillatory potentials." 

 
 

Milivoje Lukic "Square-summable variation and absolutely continuous spectrum." In Press

 
 

Milivoje Lukic, Darren C. Ong "Wigner-von Neumann type perturbations of periodic Schrödinger operators." In Press

 
 

Milivoje Lukic "On a conjecture for higher-order Szego theorems." Submitted

 
 

Milivoje Lukic "Schrödinger operators with slowly decaying Wigner-von Neumann type potentials." In Press

 
 

Milivoje Lukic "Derivatives of L^p eigenfunctions of Schrodinger operators." In Press

 
Presentations
 Invited Talks
 

"Higher-order Szego theorems." Methods of Modern Mathematical Physics, Toronto, ON, Canada. (2016/08/24)

 
 

"KdV equation with almost periodic initial data." QMath13: Mathematical Results in Quantum Physics, Atlanta, GA. (2016/10/07)

 
 

"KdV equation with almost periodic initial data." Methods of Modern Mathematical Physics, Toronto, ON, Canada. (2016/08/25)

 
 

"KdV equation with almost periodic initial data

 ." AMS Sectional Meeting, Athens, GA. (2016/03/05)