Colorful Combinatorics

Lecture notes (updated): .pdf

Exam topics: .pdf

The notes are based on less faulty books and lecture notes, notably:
Graham-Rothschild-Spencer: Ramsey Theory
Prömel: Ramsey Theory for Discrete Structures (producer: Steger)
Leader: Ramsey Theory https://www.dpmms.cam.ac.uk/~par31/notes/ramsey.pdf
de Zeeuw: A course in arithmetic Ramsey theory https://frankdezeeuw.wordpress.com/wp-content/uploads/2020/04/arithmeticramseytheory_20170506.pdf
Gasarch: Ramsey Theory and its "Applications" https://www.cs.umd.edu/~gasarch/COURSES/752/S25/index.html
Vitaly Bergelson, Florian K. Richter: Survey (NEW) https://arxiv.org/abs/2603.25922

Further recommended reading on related topics:
Lovász: Topological Methods in Combinatorics
Soifer: The new mathematical coloring book Mathematics of coloring and the colorful life of its creators
Gasarch's collection: https://www.cs.umd.edu/~gasarch/COURSES/752/S25/ramseybooks.html

1. class (15 sept): Sperner's lemma, Monsky's theorem, Envy-free division

2. class (22 sept): Tucker's lemma, Ky Fan's lemma, Necklace splitting, Kneser graphs

3. class (29 sept): Graph complexes, Hypergraph Ramsey upper bound

4. class (6 oct): Hypergraph Ramsey lower bound (Stepping-up lemma), some extra Ramsey stuff

5. class (13 oct): Erdős-Szekereses, abstract cup-cap, Schur's theorem, Hilbert's cube lemma

6. class (20 oct): van der Waerden's theorem

Fall break (27 oct): no class

7. class (3 nov): Hales-Jewett theorem, canonical vdW, Shelah's proof of HJ

8. class (10 nov): Rado's theorems except for hardest proof

9. class (17 nov): Missing proof of Rado's theorem with Deuber's theorem

10. class (24 nov): Extra Rado-related, Graham--Rothschild (without proof), Euclidean Ramsey product theorem

11. class (1 dec): Spherical and subtransitive sets in Euclidean Ramsey theory

12. class (8 dec): Cyclic transitivity implies Ramsey