## Fractional Hedetniemi’s conjecture and Chromatic Ramsey number – Ramsey DocCourse Prague 2016

The following notes are from the Ramsey DocCourse in Prague 2016. The notes are taken by me and I have edited them. In the process I may have introduced some errors; email me or comment below and I will happily fix them.

Title: Fractional Hedetniemi’s conjecture and Chromatic Ramsey number

Lecturer: Xuding Zhu

Date: November 9, 2016

Main Topics: Chromatic Ramsey numbers, lower bound for them, Hedetniemi’s conjecture, fractional Hedetniemi’s conjecture.

Definitions: $\rho$-Ramsey number, $\chi$-Ramsey number, wreath product, product graph, graph homomorphism, fractional chromatic number

## Hrushovski constructions – Ramsey DocCourse Prague 2016

The following notes are from the Ramsey DocCourse in Prague 2016. The notes are taken by me and I have edited them. In the process I may have introduced some errors; email me or comment below and I will happily fix them.

Title: Hrushovski constructions 1 (of 3)

Lecturer: David Evans

Date: November 7, 2016

Main Topics: Definition Review, $k$-very-sparse iff $k$-orientable, Existence of graph without Ramsey expansion.

Definitions: $k$-very-sparse, $k$-orientable,

## Dynamical systems and Ramsey theory – Ramsey DocCourse Prague 2016

The following notes are from the Ramsey DocCourse in Prague 2016. The notes are taken by me and I have edited them. In the process I may have introduced some errors; email me or comment below and I will happily fix them.

Title: Ergodic theory and amenable groups

Lecturer: Benjamin Weiss

Date: October 31, 2016.

Main Topics: Three equivalent notions of amenability, Basic concepts in ergodic actions, Furstenberg’s Ergodic proof of Szemerédi’s theorem

Definitions: Ergodic action, weak mixing, mixing, Banach limit, amenable group, left invariant mean, paradoxical decomposition, Følner sequence

## Functions on Homogeneous Ramsey Structures 3 – Ramsey DocCourse Prague 2016

The following notes are from the Ramsey DocCourse in Prague 2016. The notes are taken by me and I have edited them. In the process I may have introduced some errors; email me or comment below and I will happily fix them.

Title: Functions on Homogeneous Ramsey Structures 3 (of 3).

Lecturer: Michael Pinsker.

Date: Friday October 14, 2016.

Main Topics: Proof of Ramsey claim for canonical functions, Thomas’ Theorem for the Rado Graph, Open questions

Definitions: No new definitions

Lecture 1Lecture 2 – Lecture 3

## Bootcamp 6 – Ramsey DocCourse Prague 2016

The following notes are from the Ramsey DocCourse in Prague 2016. The notes are taken by me and I have edited them. In the process I may have introduced some errors; email me or comment below and I will happily fix them.

Title: Bootcamp (6 of 6)

Lecturer: Jaroslav Nesetril

Date: Monday October 3, 2016.

Main Topics: Other applications of the “product argument”, Chain-Ramsey for Posets, Proof of edge-Ramsey for Graphs, Proof of Hales-Jewett

Definitions: Structural pigeonhole principle, Poset, Graph product, Combinatorial line

Bootcamp 1 – Bootcamp 2 – Bootcamp 3Bootcamp 4Bootcamp 5 – Bootcamp 6
Continue reading Bootcamp 6 – Ramsey DocCourse Prague 2016

## Bootcamp 3 – Ramsey DocCourse Prague 2016

The following notes are from the Ramsey DocCourse in Prague 2016. The notes are taken by me and I have edited them. In the process I may have introduced some errors; email me or comment below and I will happily fix them.

Title: Bootcamp (3 of 6)

Lecturer: Jaroslav Nešetřil

Date: Friday September 23, 2016.

Main Topics: Point Ramsey for graphs, $\langle A,B,C \rangle$ hypergraphs.

Definitions: Ramsey property for finite structures, Ramsey Class, point-Ramsey, edge-Ramsey, $\langle A,B,C \rangle$ hypergraphs, Chromatic number, Ordering Property.

Bootcamp 1 – Bootcamp 2 – Bootcamp 3 – Bootcamp 4Bootcamp 5Bootcamp 6 – Bootcamp 7