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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
 Spectral theory, Schrodinger operators, integrable partial differential equations
 
Selected Publications
 Refereed articles
 

D. Damanik, J. Fillman, M. Lukic "Limit-Periodic Continuum Schrödinger Operators with Zero Measure Cantor Spectrum." J. Spectr. Theory, 7 (2017) : 1101-1118.

 
 

I. Binder, D. Damanik, M. Goldstein, M. Lukic "Almost Periodicity in Time of Solutions of the KdV Equation." Submitted

 
 

I. Binder, D. Damanik, M. Lukic, T. VandenBoom "Almost Periodicity in Time of Solutions of the Toda Lattice." C. R. Math. Rep. Acad. Sci. CanadaAccepted

 
 

J. Fillman, M. Lukic "Spectral Homogeneity of Limit-Periodic Schrödinger Operators." J. Spectr. Theory, 7 (2017) : 387-406.

 
 

Milivoje Lukic "Spectral edge behavior for eventually monotone Jacobi and Verblunsky coefficients." J. Spectr. TheoryAccepted

 
 

Yoram Last, Milivoje Lukic "ell^2 bounded variation and absolutely continuous spectrum of Jacobi matrices." Comm. Math. Phys.Accepted

 
 

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.

 
 

D. Damanik, J. Fillman, M. Lukic, 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.

 
 

D. Damanik, M. Lukic, 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.

 
 

Milivoje Lukic, Darren C. Ong "Wigner-von Neumann type perturbations of periodic Schrödinger operators." Trans. Amer. Math. Soc., 367 (2015) : 707-724.

 
 

D. Damanik, M. Lemm, M. Lukic, W. Yessen "New Anomalous Lieb-Robinson Bounds in Quasi-Periodic XY Chains." Phys. Rev. Lett., 113 (2014) : 127202.

 
 

Milivoje Lukic "A class of Schrödinger operators with decaying oscillatory potentials." Comm. Math. Phys., 326 (2014) : 441-458.

 
 

Milivoje Lukic "Square-summable variation and absolutely continuous spectrum." J. Spectr. Theory, 4 (2014) : 815-840.

 
 

Milivoje Lukic "Derivatives of L^p eigenfunctions of Schrodinger operators." Math. Model. Nat. Phenom., 8 (2013) : 170-174.

 
 

Milivoje Lukic "On a conjecture for higher-order Szego theorems." Constr. Approx., 38 (2013)

 
 

Milivoje Lukic "Schrödinger operators with slowly decaying Wigner-von Neumann type potentials." J. Spectr. Theory, 3 (2013) : 147-169.

 
 

M. Lukic "Orthogonal polynomials with recursion coefficients of generalized bounded variation." Comm. Math. Phys., 306 (2011) : 485-509.

 
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)