Since receiving my degree, my research has considered pattern formation in neural oscillators . I have focussed on models relevant to thalamic activity in sleep and paroxysmal discharges, to tremors in movement disorders such as Parkinson's disease, to respiratory rhythms, and to detection of head direction. Other recent work concerns spike-timing-dependent synaptic plasticity and traveling waves in neuronal media . Some of this work was supported by the National Science Foundation under a Postdoctoral Research Fellowship and under Grant No. 0108857.

I received my Ph.D. in May 1996. My thesis explores the generation of edge oscillations in the semiconductor Fabry-Perot interferometer using the techniques of dynamical systems. The main tools in this research are geometric singular perturbation theory and geometric methods for analyzing the stability of solutions to semilinear systems of parabolic partial differential equations. This work was done in the Division of Applied Mathematics at Brown University under the supervision of Prof. Christopher K.R.T. Jones.

Research Interests

• Pattern formation in networks of coupled neural oscillators
• Waves and localized activity generated through nonlocal interactions
• Network dynamics in the basal ganglia, with implications for motor disorders, particularly Parkinson's disease
• Mechanisms and implications of synaptic plasticity, particularly spike-timing-dependent plasticity
• Geometric singular perturbation theory and its relation to oscillations and bifurcations
• Stability of solutions to parabolic systems of partial differential equations and related equations

Publications

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