The Analysis and PDE seminar will take place Monday, October 30, in 740 Evans from 4:10 to 5pm.
Title: Inverse scattering and the Davey-Stewartson II equation
Abstract: The aim of this talk is to describe a complete implementation of the inverse scattering approach to the study of the defocusing Davey-Stewartson equation.
This will involve dispersive quations, dbar pde’s, microlocal analysis and other fun stuff. This is joint work with Adrian Nachman and Idan Regev.
The Analysis and PDE seminar will take place Monday, October 16, in 740 Evans from 4:10 to 5pm.
Title: Fractal uncertainty for transfer operators
Abstract: I will present a new explanation of the connection between
the fractal uncertainty principle
of Bourgain–Dyatlov, a statement in harmonic analysis, and the
existence of zero free strips for Selberg zeta functions, which is a
statement in geometric scattering/dynamical systems. The connection is
proved using (relatively) elementary methods via the Ruelle transfer
operator which is a well known object in thermodynamical formalism of
chaotic dynamics. (Joint work with S Dyatlov.)
The Analysis and PDE seminar will take place Monday, October 9nd, in 740 Evans from 4:10 to 5pm.
Title: Gravity water waves and emerging bottom
Abstract: To understand the behavior of waves at a fluid surface in configurations where the surface and the bottom meet (islands, beaches…), one encounters a difficulty: the presence in the bulk of the fluid of an edge, at the triple line. To solve the Cauchy problem, we need to study elliptic regularity in such domains, understand the linearized operator around an arbitrary solution, and construct an appropriate procedure to quasi-linearize the equations. Using those tools, I will present some a priori estimates, a first step to a local existence result.