Stanford University
Department of Mathematics

# Geometry Seminar Spring 2014

Organizers: Richard Bamler (rbamler@math.*) and Yi Wang (wangyi@math.*)

Time: Wednesday at 4 PM

Location: 383N

(*=stanford.edu)

## Next Seminar

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 Jean-Francois Bony, Thierry Ramond and Maher Zerzeri.

## 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 Jean-Francois 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 long-standing problem to naturally parameterized the solution space. In particular, although the set of constant mean curvature solutions is fully understood, the far-from-CMC regime is not. In this talk we describe how the two most popular competing strategies for constructing non-CMC solutions (the conformal method and the conformal thin-sandwich method) are in fact the same, and we present some examples illustrating deficiencies these methods have in constructing far-from-CMC solutions. From this analysis, we propose adjustments to the conformal method that have the potential to better describe far-from-CMC initial data.

16 April

Speaker: TBA

Title: TBA

Abstract: TBA

23 April

Speaker: Yi Wang (Stanford)

Title: Isoperimetric inequality and Q-curvature

Abstract: TBA

30 April

Speaker: TBA

Title: TBA

Abstract: TBA

9 May, Friday (Note special day and time: 11-11:50am. Regular location: 383N)

Speaker: Sun-Yung 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 Kerr-de Sitter spaces

Abstract: TBA

4 June

Speaker: TBA

Title: TBA

Abstract: TBA

## Past Quarters

For the Winter 2014 Schedule go here

For the Fall 2013 Schedule go here

For the Spring 2013 Schedule go here

For the Winter 2013 Schedule go here

For the Fall 2012 Schedule go here

For the Spring 2012 Schedule go here

For the Winter 2012 Schedule go here

For the Fall 2011 Schedule go here

For the Spring 2011 Schedule go here

For the Winter 2011 Schedule go here

For the Fall 2010 Schedule go here

For the Spring 2010 Schedule go here

For the Winter 2010 Schedule go here

For the Fall 2009 Schedule go here