Gregor Kovačič

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. 

Research Focus
  • Matematical neuroscience
  • wave dynamics
  • integrable systems
  • nonlinear resonant optics
  • optics of metamaterials
Select Works
  • 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