Program
Commuting vector fields and dispersive estimates
Student No.:50
Time:Tue/Thu 9:50-11:25, 2017-07-25~ 2017-08-03
Instructor:Willie W.-Y. Wong  [Michigan State University]
Place:Tue. Conference Room 3; Thu. Conference Room 1, Jin Chun Yuan West Building
Starting Date:2017-7-25
Ending Date:2017-8-3
 

Description:

 

Dispersive partial differential equations can be broadly characterized as those whose solutions can be expressed as a superposition of “particles” travelling at different velocities. A typical approach to proving dispersive estimates is to model particles by wave packets with restricted frequency support. Decay estimates are then obtained by exploiting the non-trivial frequency dependence of the velocity, through Fourier (stationary phase) methods. In this course we explore an alternate, physical-space oriented point of view, where particles are parametrized by their “stationary reference frames”. This leads naturally to a commuting vector field approach to understanding dispersive behavior.
 

 

 

 

Prerequisite:

 

Basic partial differential equations, basic familiarity with Sobolev spaces, basic familiarity with Fourier theory.

 

A working knowledge of fundamentals of classical and quantum mechanics will be helpful but not necessary.