Mathematics 601 (Topics in Analysis)

Harmonic analysis and the geometry of fractals

Winter/Spring 2015

Instructor: I. Laba (Math Bldg 200, 604-822-4457, ilaba(at)
Lectures: Tue Th 11-12:30, MATX 1118.
Office hours: Tue 1-2, Thur 3:30-4:30, and by appointment.

Class notes and additional references are posted here.

This course will draw on, and connect, topics from harmonic analysis, geometric measure theory, and additive combinatorics. Singular and oscillatory integrals associated with submanifolds of Euclidean spaces, and their relation to the underlying geometry, have long been a mainstay of Euclidean harmonic analysis. We will take a look at extending this line of research to the measure-theoretic setting of fractal sets, where the geometric ideas from classical harmonic analysis have arithmetic analogues inspired by additive combinatorics. Tentatively, the topics will include the following: My ICM paper has a quick preview of some of these topics, Here, we will do it more systematically and in depth. The course should provide a good foundation for anyone who might be interested in research in this area.

Your course grade will be based on an in-class presentation on a topic related to the course material. You will also have to prepare a written summary to be handed out in class. Please discuss the choice of presentation topic with me in advance, no later than February 13 (last day before the winter break). If there is a particular topic that you would like to present feel free to suggest it.

Resources: (this list will be updated as we go)
Prerequisites: MATH 541, or equivalent background in basic harmonic analysis.