Gregor Kovacic

Professor
Mathematical Sciences
518-276-6908

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. 

Education

Ph.D. California Institute of Technology, Applied Mathematics, 1990

Focus Area

Matematical neuroscience, wave dynamics, integrable systems, nonlinear resonant optics, optics of metamaterials

Selected Scholarly Works

J. W. Banks, T. Buckmaster, A. O. Korotkevich, G. Kovačič, and J. Shatah [2022]. Direct Verification of the Kinetic Description of Wave Turbulence for Finite-Size Systems Dominated by Interactions among Groups of Six Waves, Physical Review Letters 129, 034101.

Q. Xia, J.W. Banks, W.D. Henshaw, A.V. Kildishev, G. Kovačič, L.J. Prokopeva, and D.W. Schwendeman [2022]. High-order accurate schemes for Maxwell's equations with nonlinear active media and material interfaces, Journal of Computational Physics 456, 111051

K.P. Leisman, D. Zhou, J.W. Banks, G. Kovačič, and D. Cai [2022]. Improved effective linearization of nonlinear Schrödinger waves by increasing nonlinearity, Physical Review Research 4 (1), L012009.

P. B. Pyzza, K. A. Newhall, G. Kovačič, D. Zhou, and D. Cai [2021]. Network mechanism for insect olfaction, Cognitive Neurodynamics 15 (1), 103-129.

J. W. Banks, B. B. Buckner, W. D. Henshaw, M. J. Jenkinson, A. V. Kildishev, G. Kovačič, L. J. Prokopeva, D. W Schwendeman [2020]. A high-order accurate scheme for Maxwell's equations with a Generalized Dispersive Material (GDM) model and material interfaces, Journal of Computational Physics 412, 109424.

J. A. Crodelle, D. Zhou, G. Kovačič, and D. Cai [2020]. A computational investigation of electrotonic coupling between pyramidal cells in the cortex, Journal of Computational Neuroscience 48 (4), 387-407.

S. W. Jiang, G. Kovacic, D. Zhou, and D. Cai [2019]. Modulation-resonance mechanism for surface waves in a two-layer fluid system, J. Fluid Mech. 875, 807-841

G. Biondini, I. Gabitov, G. Kovacic, S Li [2019]. Inverse scattering transform for two-level systems with nonzero background, J. Math. Phys. 60 (7), 073510.

K. P. Leisman, D. Zhou, J. W. Banks, G. Kovacic, and D. Cai [2019], Effective dispersion in the focusing nonlinear Schrödinger equation, Physical Review E 100 (2), 022215.

J Crodelle, D Zhou, G Kovacic, D Cai [2019]. A role for electrotonic coupling between cortical pyramidal cells, Frontiers Comput. Neurosci. 13, 33.

A high-order accurate scheme for Maxwell's equations with a generalized dispersive material model JB Angel, JW Banks, WD Henshaw, MJ Jenkinson, AV Kildishev, G. Kovacic, L. J. Prokopeva, and D. W. Schwendeman [2019], J. Comput. Phys. 378, 411-444

W. Lee, G. Kovacic, and D. Cai [2018]. Cascade model of wave turbulence, Phys. Rev. E 97, 062140.

V. J. Barranca, G. Kovacic, D. Zhou, and D. Cai [2014]. Sparsity and compressed coding in sensory systems, PLOS Comput. Biol. 10(8), e1003793.

G. Biondini and G. Kovacic [2014]. Inverse scattering transform for the focusing nonlinear Schroedinger equation with nonzero boundary conditions, J. Math. Phys. 55(3), 031506.

Q. L. Gu, Z. K. Tian, G. Kovacic, D. Zhou, and D. Cai [2018]. The Dynamics of Balanced Spiking Neuronal Networks Under Poisson Drive Is Not Chaotic, Frontiers in Computational Neuroscience 12, 47.

S. Li, G. Biondini, G. Kovacic, and I. R. Gabitov, [2018]. Resonant optical pulses on a continuous wave background in two-level active media, Europhysics Letters 121, 2

V. J. Barranca, G. Kovacic, D. Zhou, and D. Cai [2016]. 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 [2016]. Efficient Image Processing Via Compressive Sensing of Integrate-And-Fire Neuronal Network Dynamics, Neurocomputing 171, 1313-1322.

D. Kraus, G. Biondini, and G. Kovacic [2015]. The focusing Manakov system with nonzero boundary conditions, Nonlinearity 28(9), 3101.

Associated MOCA Projects

Mathematical Neuroscience

(Modeling)

This project concerns developing theoretical models of processing taking place in a number of brain areas, mostly early sensory pathways.  One set of problems we have addressed concerns the asynchronous steady state of a sparsely, randomly connected neuronal network.   Another set of problems add

Research Training in Mathematical Modeling, Analysis and Computation

(Modeling)

This is an interdisciplinary program for undergraduates, graduate students, and postdoctoral associates that integrates modeling, analysis, and computations with contemporary experimental research.

Advanced Computational Toolkit for Engineered Optical Materials (ACTEOM)

(Computation)

ACTEOM is a DARPA funded project, part of the EXTREME program, with the goal of developing an Advanced Computational Toolkit for Engineered Optical Materials (ACTEOM).