Title: Mathematical Modeling of Neuronal Networks

Abstract:   To faithfully reproduce and explain the dynamics of networks comprising many neurons, each individual neuron can be modeled by surprisingly simple, RC-circuit-like nodes.  Sometimes even that is superfluous, and one only needs to know the activity level of a given (group of) neuron(s).  This talk will present models of this kind in detail, and then illustrate their effectiveness in proposing answers to questions such as whether our vision obeys the principle of “compressed sensing” or what is the mathematical principle underlying olfaction (i.e., how animals discriminate among different smells).

Brief Biosketch:   Gregor Kovacic 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 Preseren's Student Prize in Slovenia, Director's Funded Postdoctoral Fellowship at Los Alamos, NSF Career Award, and 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.