Brief summary: My research has mainly focused on the following problems in Statistical Mechanics:

1. Non-equilibrium collective behavior as in turbulence, aggregation and deposition in growth, transport with random inputs and outputs., etc., is best described starting from phenomenological equations constructed on the basis of symmetries and conservation laws. We have successfully applied this methodology to several problems involving polymers, flux lines, and growing surfaces.
2. Disordered systems such as spin- and flux-glasses, are characterized by a complex (free) energy landscape and slow dynamics. Using analytical solutions, or clever numerical algorithms, we have found exact results, or bounds, for a number of simple glassy systems motivated by flux lines in superconductors. Even these simple models are of great value, indicating interesting connections to diverse problems in optimization, neural networks, and evolution.
3. Biologically motivated problems such as the evolution of orientational selectivity in cells of the visual cortex, and conformations of heteropolymers.

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• Students and Postdocs
• Seminars (Presentations available on the web)
• Publications (preprints from the Archives)

(Supported by the US, National Science Foundation)

• Transversality of Natural Images