My main work is to try to understand the circuitry of the visual cortex and how it mediates visual perception. I use a combination of linear and nonlinear dynamics, symmetry groups and bifurcation theory to investigate how neural circuits can generate stable patterns of activity. The results are relevant to a wide range of observations in neurobiology and in cognitive psychology.
Another interest of mine is the mathematics of the stock market and the theory of option pricing. I am interested in the non-Gaussian aspects of price fluctuations and their origin. I use random graph theory and self-organized criticality to investigate such problems.