Research Interests

I am a multidisciplinary applied mathematician. Throughout my career I have focused on the use of mathematics in the sciences and the development of mathematics for the sciences. Modern applied mathematics includes scientific computation and numerical analysis, mathematical modeling, formal asymptotics, mathematical analysis, and direct work with experimental and observational data. I believe that applied mathematics, taken in this broadest sense, is intensely needed throughout modern science. The general area of my research is large-scale nonlinear systems - nonlinear systems whose temporal evolution is frequently described by partial differential equations. My own work provides qualitative descriptions of the temporal (regular or chaotic) behavior of specific nonlinear systems that govern idealized representations of nonlinear waves, laser beams, and most recently neuronal networks for visual neural science. In each case these are complex nonlinear systems for fields that are extended in space, and in the case of the visual cortex, composed of competing species with extensive coupling and feedback. For that system I have participated in the development of a large-scale computational model of the "front end" of the cortical visual system (the primary visual cortex) focusing upon local properties of individual cells within the large-scale network.

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Section 32: Applied Mathematical Sciences