The Analysis and PDE Seminar will take place on Monday on November 22nd 2015 from 4:10-5:00pm in Evans Hall, room 740.
Speaker: Jeremy Marzuola (UNC)
Title: Euler Equations on Rotating Surfaces
Abstract: In an appendix to a recent paper by Michael Taylor, he and I explored various questions related to stability of striated patterns for fluids on rotating spheres. I will discuss these results and some open problems related to this study.
See you all there!
Analysis and PDE seminar which will take place in 740 Evans Hall on Nov 16th
Speaker: Marina Iliopoulou (University of Birmingham)
Title: Algebraic aspects of harmonic analysis
Abstract: When we want to understand a geometric picture, finding the zero set of a polynomial hiding in it can be very helpful: it can reveal structure and allow computations. Polynomial partitioning, developed by Guth and Katz, is a technique to find such a nice algebraic hypersurface. Polynomial partitioning has revolutionised discrete incidence geometry in the recent years, thanks to the fact that interaction of lines with algebraic hypersurfaces is well-understood. Recently, however, Guth discovered agreeable interaction between tubes and algebraic hypersurfaces, and thus used polynomial partitioning to improve on the 3-dim restriction problem. In this talk, we will present polynomial partitioning via a discrete analogue of the Kakeya problem, and discuss its potential to be extensively used in harmonic analysis.
Monday, Nov 9th 2015
Evans Hall, Room 740
Speaker: Baoping Liu, (Peking University)
Titile: Long time dynamics for wave equation with potential
Abstract: We consider the long time dynamics of radial solutions to the defocusing energy critical wave equation with radial potential in 3+1 dimensions. For general potential, the equation can have a unique positive ground state and a number of excited states. In this talk, we show that for generic potential, generic radial solutions scatter to one of the stable steady states and each unstable excited state attracts a finite co-dimensional manifold of solutions. This gives affirmative answer to the soliton resolution conjecture for this particular model.
This talk is based on joint works with Hao Jia, Wilhelm Schlag and Guixiang Xu.