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Transcript
Distinguished Lecturer Series Special Event Sponsored by the Arthur and Rochelle Belfer Institute of Mathematics and Computer Science Sunday, 31 October 2010 Room 1, Ziskind Building 14:30 - 15:30 Constantine Dafermos Brown University Maximal Dissipation in Equations of Evolution Abstract: The lecture will introduce examples of evolutionary equations with diverse provenances, in which a certain energy functional is conserved along classical solutions, the initial value problem generally admits a multitude of weak solutions, and argue that the solution along which the energy decays at a maximum rate may have special status. 15:30 - 16:00: Coffee break 16:00 - 17:00 Srinivasa Varadhan New York University Large Deviations for Random Graphs Abstract: In this joint work with Sourav Chatterjee, we consider a random graph with n vertices, with probability p for any given edge to be present. We consider the case when p is fixed and n gets large. Asymptotically the expected number of edges is ~1/2 n2 and the expected number of triangles is ~1/6 n3. We look at the large deviation probabilities for these numbers as well as other subgraph counts. This allows us to say, for example, what a graph with more than the normal number of triangles will look like. The model exhibits an interesting phase transition.