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The Propagation of Oscillations: Some New/Old Perspectives

By Nick Ercolani, University of Arizona

Methods of nonlinear steepest descent have proved effective in developing normal form for the propogation of oscillations in a nonlinear environment. This talk will focus on the birth of such oscillations within the framework of random matrix theory and its applications to generating functions for random combinatorial structures relating to older perspectives on dispersive limits of integrable PDE such as the nonlinear Schrodinger equation.