Date: Tuesday, November 16, 2021
Location: 1360 East Hall (4:00 PM to 5:00 PM)
Title: Randomness in nonlinear dispersive equations
Abstract: Randomness is ubiquitous in nature. It is exhibited in mathematics in a wide range of models and problems from different areas. From the point of view of PDEs, there are three main phenomena we are interested in: statistical description of the system, propagation of randomness, and stochastic regularization. I will talk about a series of recent works in nonlinear dispersive equations related to these three phenomena. Using the nonlinear Schrodinger equation as a model, I will discuss the dynamics of Gibbs measure (equilibrium statistical mechanics), mathematical treatment of wave turbulence (nonequilibrium statistical mechanics), and uniqueness of rough solutions. These are joint works with Zaher Hani, Andrea Nahmod, and Haitian Yue.
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Speaker: Yu Deng
Institution: University of Southern California
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