Mathematics Colloquia and Seminars

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This lecture blends ideas from probability theory, PDE’s, numerical analysis and physical reasoning in the style of modern applied mathematics. First elementary concepts of information theory involving the lack of information in one probability measure relative to another are introduced. These ideas are then applied to give a unified explanation of the competing equilibrium statistical theories for coherent structures in fluids. The potential application of these ideas to predict coherent structures in flows with random forcing and dissipation is then discussed briefly including the first theorem (Xiaoming Wang and Majda, CPAM 2006) justifying the approach. All of this is utilized to develop a successful prediction for the exact location and structure of Jupiter’s Red Spot in agreement with the Voyager Mission of the 1970’s by utilizing a physically based prior encoding the key features of small scale observations from the Galileo mission of the 1990’s. An apriori independent justification of this overall strategy is presented though novel numerical methods for detecting statistically relevant conserved quantities in fluid flow (Abramov and Majda, 2003, 2004.)

Note: The Applied Math Seminar is joint with the the Mathematics Colloquium this week.