Math 264A (Fall 2020)
Summary
This is a graduate course in combinatorics. I will focus on topics in extremal combinatorics and extremal graph theory, with a particular theme of infinitary methods, analytic methods, the regularity lemma and quasirandomness.
The overall theme is to try to give an indication of how methods from infinitary mathematics, analysis, measure theory etc. can be used to solve otherwise difficult combinatorial problems; and to explain how to translate between the finitary and infinitary worlds.
The exact list of topics to be covered will remain fluid and influenced by popular opinion, but is likely to include:–
- Ramsey problems and compactness;
- quasirandomness in graphs and its many definitions;
- Szemerédi's regularity lemma and counting lemmas;
- triangal removal &s; Roth's theorem;
- the Erdős–Stone theorem;
- graphons and graph limits;
- flag algebras;
- ...
Contacts
The instructor is Freddie Manners (email fmanners; my office is AP&M 7343, but don't go there).
Class and office hours
Lectures are held on Mondays, Wednesdays and Fridays, 0900–0950. Lectures will be held via Zoom. See Canvas for the Zoom links.
I will hold regular office hours as follows:—
| Mondays | Wednesdays | Fridays |
| 11:00 AM – 12:00 AM | 2:00 PM – 3:00 PM | 10:00 AM – 11:00 AM |
A calendar is provided below for your convenience, and may be updated from time to time to reflect changes to this schedule.
Please note that all lectures, sections and office hours may be recorded in Zoom and reposted to the class.
Virtual attendance in class is mandatory and carries credit; see below. However, exceptions can be made if your timezone or circumstances make this logistically difficult. In that case, you can arrange to attend the lectures "doubly virtually" at another time. You must contact the lecturer to arrange this option, or discuss other logistical difficulties.
Grading
The grading for the class will be based on attendance (10%) and homework assignments (90%).
Homework assigments will be conducted asynchronously: they may be submitted at any time during the quarter.
Note that homework is held to high standards of academic integrity. Discussing homework with your peers is acceptable, but your solutions must be written by you alone, in your own words. Soliciting help with homework on the internet is a serious AI violation.
Undergraduates taking the course are strongly encouraged to discuss grading expectations with the instructor at the start of the quarter, and to attend office hours as often as possible.
While homework can — technically — be submitted at any time, the following take provides expectations about when homework will be released, and ideally returned.
| No | Release Date | Return Date (?) |
| 1 | Monday October 12 | Around October 26 |
| 2 | Monday October 26 | Around November 9 |
| 3 | Monday November 9 | Around November 23 |
| 4 | Monday November 23 | Ideally December 11 (last day of class) |