## Partite constructions 2 – 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: Partite consturctions 2 (of 3)

Lecturer: Jaroslav Nešetril

Date: Tuesday October 25, 2016.

Main Topics: There are graphs with large chromatic number but no small cycles, Tutte’s construction, Edge-Ramsey for graphs (using partite construction)

Definitions: No New definitions.

Part 1 – Part 2 – Part 3

## Ramsey and Ultrafilters 2 – 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.

Special thanks to Ivan Khatchatourian for some elaborations.

Title: Ramsey and Ultrafilters 2 (of 2)

Lecturer: Slawomir Solecki

Date: Friday October 21, 2016.

Main Topics: Abstraction of Gowers/Lupini/Furstenberg-Katznelson, worked example with Furstenberg-Katznelson, slides about tensors

Definitions: Forestation of a Poset, Semigroup generated by a poset, [Specific to these constructions], $\hat{Y^{\prime\prime}(M)}$

Lecture 1 – Lecture 2

You might also be interested in Solecki’s independent lecture about projective Fraisse limits [link soon].
Continue reading Ramsey and Ultrafilters 2 – Ramsey DocCourse Prague 2016

## Ramsey and Ultrafilters 1 – 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.

Special thanks to Ivan Khatchatourian for clarifying some typos and adding some elaborations.

Title: Ramsey and Ultrafilter 1 (of 2)

Lecturer: Slawomir Solecki

Date: Wednesday October 19, 2016.

Main Topics: Gowers’ Theorem, Lupini’s Theorem, Furstenberg-Katznelson Theorem, Monoids, Semigroups.

Definitions: [many]

Lecture 1 – Lecture 2

You might also be interested in Solecki’s independent lecture about projective Fraisse limits [link soon].
Continue reading Ramsey and Ultrafilters 1 – Ramsey DocCourse Prague 2016

## Bootcamp 8 – 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 8 (of 8)

Lecturer: Jan Hubička

Date: Wednesday October 12, 2016.

Main Topics: Ramsey lifts, Classification results, Tournaments, Digraphs, Permutations, unary functions, Steiner Systems, Dual Ramsey, Graham-Rothschild.

Definitions: Digraph, Tournament, Interposition, $\text{CSP}(G)$, Strong substructure, unary function, Steiner System

Bootcamp 1Bootcamp 2Bootcamp 3Bootcamp 4Bootcamp 5Bootcamp 6Bootcamp 7 – Bootcamp 8

Note: The material here is meant as an overview, so many details are missing.
Continue reading Bootcamp 8 – Ramsey DocCourse Prague 2016

## 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 7 – 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 7 (of 8)

Lecturer: Jan Hubička

Date: Monday October 10, 2016.

Main Topics: “Correct” definition of Ramsey expansion, Ramsey lifts/expansions of graphs, Ramsey lifts/expansions of posets.

Definitions: Precompact expansion, Expansion property, Free Amalgamation, strong type, equivalence formula, equivalence closure, interpretation in a model.

Bootcamp 1 – Bootcamp 2 – Bootcamp 3Bootcamp 4Bootcamp 5Bootcamp 6 – Bootcamp 7 – Bootcamp 8

INCOMPLETE: One dimensional proof of $t$ copies of $K_\omega$, $\omega$ copies of $K_\omega$.

## Functions on Homogeneous Ramsey Structures 2 – 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.

Special thanks. Thank you to Michael Kompatscher for all his feedback and helpful comments.

Title: Functions on Homogeneous Ramsey Structures 2 (of 3).

Lecturer: Michael Pinsker.

Date: Friday October 7, 2016.

Main Topics: Equivalent notions of $\omega$-categorical, Proof of Cameron’s Theorem, Proof of canonical-Ramsey.

Definitions:No new ones.

Lecture 1 – Lecture 2 – Lecture 3