Ramsey theory
Spring 2024, ETH Zürich
Lectures: Wednesdays, 12:15–14:00, HG D 5.2.
Lecture recordings should be at this link.
The course has a Moodle site. However, it will always have the same information as this site, so you can check either one.
The course also has a forum.
Lecture notes (last updated 18/6/2024)
Practice Exam
The practice exam is here. Like the real exam, it has six problems and is meant to be solved in 3 hours.
Solutions to the practice exam are here.
Homework
- Homework 1, released February 19
- Homework 2, released February 27
- Homework 3, released March 6
- Homework 4, released March 13
- Homework 5, released March 19
- Homework 6, released March 26
- Homework 7, released April 9
- Homework 8, released April 17
- Homework 9, released April 23
- Homework 10, released May 8
- Homework 11, released May 15
- Homework 12, released May 21
Solutions to selected exercises — send me an email if you would like a solution to a certain problem!
Syllabus
- Feb 21: Introduction, classical bounds on Ramsey numbers
- Feb 28: Lower bounds on multicolor Ramsey numbers
- Mar 6: Off-diagonal Ramsey numbers—upper bounds
- Mar 13: Off-diagonal Ramsey numbers—lower bounds
- Mar 20: Graph Ramsey numbers—trees, complete bipartite graphs, sparse graphs
- Mar 27: Ramsey numbers of sparse graphs and the regularity method in Ramsey theory
- Apr 3: no lecture (Easter holiday)
- Apr 10: Restricted Ramsey graphs and the induced Ramsey theorem
- Apr 17: The Erdős–Szemerédi multicolor problem and the structure of C-Ramsey graphs
- Apr 24: The Hales–Jewett theorem: statement and applications
- May 1: no lecture (Labour day)
- May 8: The Hales–Jewett theorem: more applications and proof
- May 15: Hypergraph Ramsey numbers—stepping up and stepping down
- May 22: Points in convex position, monotone subsequences, and the canonical Ramsey theorem
- May 29: The book algorithm