
MATH 601:
Introduction
to Microlocal Analysis


Microlocal analysis is a
geometric theory of distributions, describing techniques developed
during the past centuary based on Fourier transforms related to the
study of inear and nonlinear partial differential equations. This
includes generalized functions, pseudodifferential operators and
Fourier integral operators. The term microlocal implies localisation
not just at a point, but in terms of cotangent space directions at a
given point.
The main topics of the course are:
1. Theory of distributions.
2. Method of stationary phase
3. Pseudodifferential operators.
4. Application to elliptic operators
5. The zeta function of an elliptic operator.
6. Asymptotic behavior of the spectral counting function.
Announcements:

09/04/2009  Website
Created.
09/27/2009  Assignment 1 Posted.

Instructor:

Prof. Mahta Khosravi

Office Hours

M (Monday) 12:00pm  1:00pm (MATH
219)
F
(Friday) 1:00pm  2:00pm (MATH 219) 
Time and Location:

MWF 2:00pm  3:00pm (Math Annex 1102)

Text:

“Microlocal
Analysis for Differential Operators: An Introduction." by A. Grigis and
J. Sjöstrand.

Homework and Exams:

There will be no formal exams. Homework problems will be posted
regularly on the course website. Towards the end of the term everybody
will make a 30 minute presentation. The topics for the presentations
will be given during the lectures.
50% on the homework
50% Class presentations

