Spring Quarter


2 April

Speaker: Setsuro Fujiie (Ritsumeikan University) (Analysis and PDE Seminar)
Title: Semiclassical distribution of resonances created by homoclinic trajectories
Abstract: We consider the Schrödinger operator \( −h^2 \Delta + V (x) \) in the multidimensional Euclidean space with a semiclassical parameter h and a smooth potential decaying at infinity. Assuming that the underlying classical mechanics on the energy surface of a fixed positive energy has a trapped set consisting of homoclinic trajectories, we describe the precise asymptotic distribution of resonances in a complex neighborhood of this energy. The method is based on the microlocal study of solutions near the trapped set, especially near the hyperbolic fixed point. This is a joint work with JeanFrancois Bony, Thierry Ramond and Maher Zerzeri.

9 April

Speaker: David Maxwell (Fairbanks)
Title: Initial Data in General Relativity Described by Expansion and Conformal Deformation
Abstract: Initial data for the vacuum Cauchy problem in general relativity satisfy a system of nonlinear PDEs known as the Einstein constraint equations. These equations are underdetermined, and it has been a longstanding problem to naturally parameterized the solution space. In particular, although the set of constant mean curvature solutions is fully understood, the farfromCMC regime is not. In this talk we describe how the two most popular competing strategies for constructing nonCMC solutions (the conformal method and the conformal thinsandwich method) are in fact the same, and we present some examples illustrating deficiencies these methods have in constructing farfromCMC solutions. From this analysis, we propose adjustments to the conformal method that have the potential to better describe farfromCMC initial data.

16 April

Speaker: TBA
Title: TBA
Abstract: TBA

23 April

Speaker: Yi Wang (Stanford)
Title: Isoperimetric inequality and Qcurvature
Abstract: TBA

30 April

Speaker: TBA
Title: TBA
Abstract: TBA

9 May, Friday (Note special day and time: 1111:50am. Regular location: 383N)

Speaker: SunYung Alice Chang (Princeton)
Title: TBA
Abstract: TBA

14 May

Speaker: TBA
Title: TBA
Abstract: TBA

19 May MONDAY (Note special seminar)

Speaker: TBA
Title: TBA
Abstract: TBA

28 May

Speaker: Peter Hintz (Stanford)
Title: Nonlinear wave equations on de Sitter and Kerrde Sitter spaces
Abstract: TBA

4 June

Speaker: TBA
Title: TBA
Abstract: TBA
