Dual Ramsey, an introduction – 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: Dual Ramsey, the Gurarij space and the Poulsen simplex 1 (of 3).

Lecturer: Dana Bartošová.

Date: December 12, 2016.

Main Topics: Comparison of various Fraïssé settings, metric Fraïssé definitions and properties, KPT of metric structures, Thick sets

Definitions: continuous logic, metric Fraïssé properties, NAP (near amalgamation property), PP (Polish Property), ARP (Approximate Ramsey Property), Thick, Thick partition regular.

Lecture 1 – Lecture 2 – Lecture 3

Ramsey DocCourse Prague 2016 Index of lectures.

Bootcamp 1 – Ramsey DocCourse Prague 2016

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

Title: Bootcamp 1 – Informal meeting.

Lecturer: Jaroslav Nešetřil.

Date: September 20, 2016.

Main Topics: Overview over the topics of the DocCourse; classical result in Ramsey theory

Definitions: Arrow notation, Ramsey numbers, arithmetical progression

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

Bootcamp 2 – Ramsey DocCourse Prague 2016

The following notes are from the Ramsey DocCourse in Prague 2016. The notes were taken and edited by myself and Michael Kompatscher. In the process we may have included some errors; email us or comment below and we will happily fix them.

Title: Bootcamp 2 (of 8)

Lecturer: Jaroslav Nešetřil.

Date: September 21, 2016.

Main Topics: The Rado graph, homogeneous structures, universal graphs

Definitions: Language, structures, homomorphisms, embeddings, homogeneity, universality, Rado graph (Random graph),…

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

Introduction to the KPT correspondence 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: Introduction to the KPT correspondence 3 (of 3).

Lecturer: Lionel Ngyuen Van Thé.

Date: November 18, 2016.

Main Topics:

Definitions: Expansion property,

Lecture 1Lecture 2 – Lecture 3

Topological dynamics and Ramsey classes – 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: Topological dynamics and Ramsey classes.

Lecturer: Lionel Ngyuen Van Thé.

Date: November 14, 2016.

Main Topics: Proof of KPT correspondence between extreme amenability and ramsey class.

Definitions: Topological group, $S_\infty$, $d_R, d_L$, Polish group, ultrametric, $G$-flow, extreme amenability.