Office: 383M
Phone: 723-2226
E-mail: andras "at" math.stanford.edu
Tentative office hours: MT 11am-12pm, Th1-2pm.
Class location: MWF 12:50-2:05pm, Room 380D. The class will meet twice per week on average; three days are listed to help with scheduling conflicts.
Textbook: `Geometric scattering theory' by R. B. Melrose and volume 2 of Michael Taylor's `Partial differential equations', both recommended.
A knowledge of microlocal analysis, as presented in 256B in Winter 2011, is NOT a pre-requisite. I will provide a quick overview when needed. For a more thorough background on this, please see Richard Melrose's lecture notes and volume 2 of Michael Taylor's PDE book.
This is an advanced graduate PDE class, focusing on scattering theory, but no PDE background is required. (Thus, 256A is not a prerequisite.) However, a thorough knowledge of functional analysis and Fourier analysis (as presented in the Math 205 sequence) is a must. Very strong students can take 205B concurrently with 256B; this requires permission of the instructor.In physics, scattering theory describes the long-time behavior of particles/waves. Mathematically, it either corresponds to the asymptotic behavior of solutions of evolution equations (such as the wave or the Schrödinger equation) or to the asymptotic behavior of generalized eigenfunctions for the associated spatial (elliptic) problem. We start with potential scattering on Euclidean space to understand the motivations and the basic framework without needing sophisticated analytic tools. Later we work with asymptotically Euclidean/conic spaces, asymptotically hyperbolic spaces, perhaps even cusps, and possibly some quantum N-particle scattering.
Grading policy: There may be a few problem sets which must be handed in, but due to unavailability of graders, will not be graded carefully.
The homework will be due either in class or by 9pm in the instructor's mailbox on the designated day. You are allowed to discuss the homework with others in the class, but you must write up your homework solution by yourself. Thus, you should understand the solution, and be able to reproduce it yourself.