Bio: Christoph Börgers is a Professor of Mathematics at Tufts University. He got his Ph.D. under Prof. Charles Peskin at the Courant Institute of Mathematical Sciences, in 1985. Prof. Börgers was a professor in the University of Michigan department of Mathematics until 1996 when he moved to Tufts. His expertise is in mathematical neuroscience, applied dynamical systems, numerical analysis, scientific computing, and during the past decade, most of his work has been in the area of Computational Neuroscience.

Rhythms in neuronal networks with recurrent excitation

Interacting excitatory and inhibitory neuronal populations often generate oscillations in electrical fields in the brain. I will briefly review this mechanism and the reasons to believe that it is important in brain function. Most of the talk will be focused on the effects of recurrent excitation, i.e., of the neurons of a local network in the brain exciting each other. Recurrent excitation can sustain activity in a network that would otherwise be quiescent; this is believed to be the basis of working memory. It can also lead to a runaway process, with excitation generating more excitation etc., much as the presence of a quadratic term on the right-hand side of a differential equation can lead to blow-up in finite time; this may be related to epileptic seizures. For model problems, we prove that abrupt transitions to runaway activity require recurrent excitation with fast kinetics, while working memory activity is more robust with recurrent excitation with slow kinetics.

Prof. Börgers is being hosted by Prof. Robert Krasny (Mathematics).