Mathematics 601E: Topics in Analysis, Winter/Spring 2020

Decoupling theory

Section 201: MWF 10:00-10:50, MATX 1102. Credit value: 3 credits.

Instructor: Professor I. Laba Prerequisites: MATH 420/507 and 404/541, or equivalent background in real and harmonic analysis.

Course structure: 3 lecture hours per week, supplemented by office hours, regular homework, and discussion boards on Canvas and Piazza. There will also be opportunities to ask questions during class.

Required learning materials: There is no required textbook for the course. Suggested and recommended reading materials are as follows.

Presentation handouts:

Course topics and learning objectives: Decoupling theory is a timely and exciting area of harmonic analysis. Its origins go back to the work of Wolff in the early 2000s, but the current form of decoupling theory was developed more recently, starting with the work of Bourgain and Demeter on the decoupling conjecture for the sphere. Decoupling methods have led to major advances in both harmonic analysis (restriction theory) and number theory (Vinogradov's conjecture), including the work of Bourgain, Demeter, Guth, and others. There is a significant and sustained interest among mathematicians in learning the subject. The proposed course will focus on the harmonic-analytic side of decoupling. We will be aiming towards the proof of the Bourgain-Demeter theorem, with the necessary background and techniques. The course will be modelled in part on the two graduate courses taught by Larry Guth at MIT, and should be accessible to all students who have taken MATH 541 or have equivalent background.

Tentative schedule: Detailed updates on class topics covered each week and reference materials are posted here

Your course mark will be based on a presentation of a suitable topic in decoupling theory, chosen in consultation with the instructor. Either a written submission or an oral presentation in class will be acceptable.

Academic concession: The rules and procedures for obtaining academic concession are governed by UBC Policy V-135 on Academic Concession. The presentation deadlines in this class will be flexible, so there should not be a problem with obtaining an extension if necessary.

Academic misconduct: UBC takes cheating incidents very seriously. After due investigation, students found guilty of cheating on tests and examinations are usually given a final grade of 0 in the course and suspended from UBC for one year. See here for more information. Statement about the University's values and policies, mandated by UBC Policy V-130: UBC provides resources to support student learning and to maintain healthy lifestyles but recognizes that sometimes crises arise and so there are additional resources to access including those for survivors of sexual violence. UBC values respect for the person and ideas of all members of the academic community. Harassment and discrimination are not tolerated nor is suppression of academic freedom. UBC provides appropriate accommodation for students with disabilities and for religious, spiritual and cultural observances. UBC values academic honesty and students ae expected to acknowledge the ideas generated by others and to uphold the highest academic standards in all of their actions. Details of the policies and how to access support are available here.
[Mathematics Department] [University of British Columbia]