The HADES seminar on Tuesday, September 29th will be given by Maciej Zworski via Zoomfrom 3:40 to 5 pm.

Speaker: Maciej Zworski

Abstract: As analysts we are used to smooth functions of compact support and after constructing one example of a bump function we are happy to apply it for many purposes. We also know that for any sequence of numbers we can construct a smooth function with that sequence as coefficients of its Taylor series. Can that map from sequences to functions be made linear? The answer is no for all sequences but yes for sequences satisfying certain growth conditions. I will prove the Denjoy–Carleman theorem which shows what growth is needed if you want to keep compact support, describe Carleson’s moment problem and talk about characterization of an important subclass of Gevrey functions. Those functions appear naturally in the theories of diffraction, of Landau diffusion for the Boltzmann equation, and of trace formulas for Anosov flows.

The HADES seminar on Tuesday, September 8will be given by James Rowan via Zoom (please contact the organizer at “james_rowan at berkeley dot edu” for the Zoom ID) from 3:40 to 5 pm.

Speaker:  James Rowan

Abstract:  I will present a recent paper by Merle, Raphael, Rodnianski, and Szeftel which constructs a new kind of blowup solution for certain supercritical nonlinear Schrodinger equations.  The mechanism is neither a rapid frequency cascade nor concentration of a [quasi]soliton, but rather a highly-oscillatory front blowup coming from a collection of special solutions to the self-similar spherically symmetric Euler equations.  The construction relies on studying the behavior of a wave equation in the phase and modulus variables and a fixed point argument to control the behavior of unstable modes.  Along the way I hope to showcase some common techniques in the study of nonlinear PDEs.