Terence Tao will be teaching online course Classical Fourier Analysis at UCLA from 30 March 2020.
Course covers the following topics:
- Restriction theory and Strichartz estimates
- Decoupling estimates and applications
- Paraproducts; time frequency analysis; Carleson’s theorem
Lecture notes will be made available on this blog.
- The first class is Monday Mar 30.
- Note for non-UCLA participants: You will be permitted to attend the Zoom lectures and to post comments on the blog (one can use this post in particular for general questions about the course).
- Instructor: Terence Tao, firstname.lastname@example.org, MS 6183. [Note for non-UCLA participants: I will not have time to respond to individual email inquiries about the class. Please use the blog for such inquiries.]
- Lecture: MWF 2-2:50pm PT, held online at https://ucla.zoom.us/j/9264073849 . Note that access to this Zoom meeting room may be restricted outside of lecture times, or used for other purposes (such as other online seminars). Also, while I am not recording these classes, bear in mind that I cannot prevent the video for these rooms from theoretically being recorded by third parties.
- Discussion section: N/A
- Office Hours: Th 2-3:50pm PT, online at https://ucla.zoom.us/j/9264073849 In addition, students are encouraged to use the blog comment feature, as well as start discussions in the forum. [Note for non-UCLA participants: you have read-only access to the forum. You can use the comment thread at this blog post as a substitute.]
- Textbook: There is no required text; instead, lecture notes will made available on Terence Tao’s blog. We will not directly follow these texts, but Demeter’s “Fourier Restriction, Decoupling, and Applications” and Muscalu-Schlag’s “Classical and multilinear harmonic analysis” (both volumes) will be relevant resources. For Carleson’s theorem, this paper of Demeter (focusing on the slightly simpler Walsh model analogue of the theorem) can also be consulted.
- Prerequisites: A high grade in Math 247A (such as the previous quarter’s class) is required for enrollment. [Note for non-UCLA participants: Math 247A covered the following topics: A_p weights and maximal and vector maximal functions, Calderon-Zygmund convolution kernels, Sobolev embedding, the Mikhlin multiplier theorem, the square function, Littlewood-Paley theory, fractional product and chain rules, and oscillatory integrals.]