L24 Math 523 (Topics in Analysis: Geometric Measure Theory) Syllabus
This is the class webpage and syllabus for Math 523 in Spring 2020. Any changes or updates to the syllabus will be posted here and will be announced in class.
Course Information
- Instructor: Dr. Tyler Bongers, tyler.bongers@wustl.edu
- Office hours: 1:30-2:30 PM Monday; 1-2 PM Tuesday; 9:30 - 10:30 AM Friday; by appointment; Cupples I 203.
- Course location and times: Cupples I, Room 215; TTh 2:30-3:50 PM.
Course Description
This course will cover various topics of importance in geometric measure theory, including covering lemmas, Hausdorff measure and dimension, density results for measures, capacities, projection theory, Fourier transforms of measures and distance sets, rectifiability, and the connection between rectifiability and singular integrals.
The textbook for the course is Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability by Pertti Mattila.
Another resource for the course (as well as a great overview of the connections between rectifiability, capacity, and singular integral theory) is
Analytic Capacity, Rectifiability, and Menger Curvature by Hervé Pajot.
During the last few weeks of the course, each participant should choose a paper (in consultation with the instructor) related to geometric measure theory and give a 50 minute presentation on the main ideas and some techniques from the paper. If you aren't sure of a paper that you would like to talk about, I am very happy to suggest one.
Other Course Policies and Helpful Information
Washington University is committed to providing accommodations and/or services to students with documented disabilities. Students who are seeking support for a disability or a suspected disability should contact Disability Resources at 935-4153. Disability Resources is responsible for approving all disability-related accommodations for WU students, and students are responsible for providing faculty members with formal documentation of their approved accommodations at least two weeks prior to using those accommodations. I will accept Disability Resources VISA forms by email and personal delivery. If you have already been approved for accommodations, I request that you provide me with a copy of your VISA within the first two weeks of the semester.
