Math 262A (Spring 2026): Hypercontractivity / Spreadness
Summary
This is a graduate topics class in combinatorics. The goal of the course is to cover some recent breakthroughs across combinatorics using one of the techniques of "spreadness" or "(global) hypercontractivity". I'm particularly interested in the relationship and parallels between these two seemingly disparate tools.
Some examples of topics we are likely to cover in some order (subject to change / whim):—
- the Kelley–Meka bounds on Roth's theorem;
- work of Alweiss–Lovett–Wu–Zhang on the Sunflower Conjecture;
- Green–Sawhney's bounds in the Furstenberg–Sárköaut;zy theorem;
- Keevash–Lifschitz–Minzer on the largest product-free subsets of the alternating group;
- thresholds and the resolution of the Kahn–Kalai and Talagrand conjectures;
- older results on hypercontractivity and log-Sobolev inequalities in relation to random walks.
Contacts
The instructor is Freddie Manners (email fmanners); my office is AP&M 7343. There is no TA for this class.
Class and section
Lectures are held on Tuesdays and Thursdays, 1500–1620 (i.e., 3pm–4:20pm). They will be held in-person in AP&M 7321.
Note there will not be in-person class on April 30. The class will either be rearranged or replaced with an equally exciting activity, TBD.
Course grading
In all mathematical study at any level, successful absorption of the material depends on solving written problems. Accordingly, two or more problem sheets will be assigned throughout the quarter.
The course grade will be assessed based on:
- submission of written solutions to certain of these problems; and
- an in-class presentation on the student's solutions to one of the nominated "substantial" problems from these collections.
These presentations will likely occur during class in week 10. Students with questions about grading expectations in this course, and enrolled undergraduates having questions or not, should discuss this with the instructor directly.
Resources
The instructor will likely place written notes on the course Canvas page. Any further course websites will be linked from the syllabus page on Canvas.
Office hours
Regular office hours and locations are listed in the table below. However, please check the calendar below for any one-off changes or cancellations.
| Instructor / TA | Location | Regular hours |
|---|---|---|
| Freddie Manners | APM-7343 | TBD |
Course calendar
A link to add this calendar is available on the course's Canvas page.