Professor, Mathematical Sciences
Gregor Kovačič received batchelor's degrees in Physics and Mathematics from the University of Ljubljana, Slovenia, and a Ph.D. in Applied Mathematics from California Institute of Technology. He was a Postdoctoral Fellow at the Los Alamos National Laboratory before joining the Mathematical Sciences Faculty at Rensselaer. Gregor is the recipient of a Prešeren's Student Prize in Slovenia, a Director's Funded Postdoctoral Fellowship at Los Alamos, an NSF Career Award, and a Sloan Research Fellowship.
Gregor's research began in low-dimensional dynamical systems, in particular, in singular perturbation theory of systems with internal resonances. His current research interests include studies of nonlinear evolution equations and their scientific applications, particularly in dispersive waves, optics, and neuroscience. Recently, he has been exploring dynamics and statistics of dispersive wave-like and completely integrable partial differential equations and their applications to nonlinear resonant optics, light propagation through “metamaterials” with exotic properties of the refractive index, and the modeling of and dynamics in neuronal networks.
- Matematical neuroscience
- wave dynamics
- integrable systems
- nonlinear resonant optics
- optics of metamaterials
- V. J. Barranca, G. Kovacic, D. Zhou, and D. Cai . Improved Compressive Sensing of Natural Scenes Using Localized Random Sampling, Nature Scientific Reports 6, 31976.
- V. J. Barranca, G. Kovacic, D. Zhou, and D. Cai . Efficient Image Processing Via Compressive Sensing of Integrate-And-Fire Neuronal Network Dynamics, Neurocomputing 171, 1313-1322.
- D. Kraus, G. Biondini, and G. Kovacic . The focusing Manakov system with nonzero boundary conditions, Nonlinearity 28(9), 3101.
- G. Biondini and G. Kovacic . Inverse scattering transform for the focusing nonlinear Schroedinger equation with nonzero boundary conditions, J. Math. Phys. 55(3), 031506.
- W. Lee, G. Kovacic, and D. Cai . Generation of Dispersion in Non-Dispersive Nonlinear Waves in Thermal Equilibrium, Proc. Natl. Acad. Sci. U.S.A. 110(9), 3237-3241.
- A. O. Korotkevich, K. E. Rasmussen, G. Kovacic, V. Roytburd, A. I. Maimistov, and I. Gabitov . Optical Pulse Dynamics in Active Metamaterials with Positive and Negative Refractive Index, JOSA B 30(4), 1077-1084.
- E. P. Atkins, P. R. Kramer, G. Kovacic, and I. Gabitov . Stochastic Pulse Switching in a Degenerate Resonant Optical Medium, Phys. Rev. A 85, 043834.