UBC

MATH 601:

Introduction to Microlocal Analysis


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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, pseudo-differential 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. Pseudo-differential 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

This page last modified Sun Jan 4 11:30pm 2009