Some material is covered in my notes on multicolour Ramsey Numbers. We also recommend the survey of Conlon, Fox and Sudakov and the more recent surveys of Morris and Verstraete.
We also provide on the recent breakthrough of Bradač, which shows that, up to polylog terms R(t,k) grows at least as fast as k^{t-2}, for any fixed t.
Version 1 of the notes (as presented at the summer school)
Version 2 of the notes (with the new lower bound k^{t-1})
The main aim of the course is to give a full proof of the new exponential improvement on the upper bound of multicolour Ramsey Numbers. We also include a discussion of techniques that have recently been used to improve lower bounds. All six lectures are available on YouTube. Link to the first lecture: https://youtu.be/Go_zaLF4SqI?si=uvHBL3tN7avYYVrt
Lecture 1: Lower bounds
Lecture 2: Lower bounds continued, and discussion of two colour upper bounds
Lecture 3: Discussion of the new proof
Lecture 4: The Geometric Lemma
Lecture 5: The Books Algorithm and its properties
Lecture 6: Completing the proof
Lecture notes for the mini-course are available here and include a full proof of the new upper bound in the case of 3 colours.
Fichas de Exercícios:
Fichas de Exercícios: