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

Continue reading Introduction to the KPT correspondence 3 – Ramsey DocCourse Prague 2016

## Introduction to the KPT Correspondence 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**: Introduction to the KPT correspondence 2 (of 3).

**Lecturer**: Lionel Ngyuen Van Thé.

**Date**: November 16, 2016.

**Main Topics**: Computing universal minimal flows, , why precompactness is important.

**Definitions:** Minimal flow, universal flow, Logic action, -equivariant.

Lecture 1 – Lecture 2 – Lecture 3

Continue reading Introduction to the KPT Correspondence 2 – Ramsey DocCourse Prague 2016

## 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, , , Polish group, ultrametric, -flow, extreme amenability.

Continue reading Topological dynamics and Ramsey classes – Ramsey DocCourse Prague 2016

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

**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:** -Ramsey number, -Ramsey number, wreath product, product graph, graph homomorphism, fractional chromatic number

## The first dynamical system; Random Number Theory – Ramsey Doccourse Prague 2016

**Title**: The first dynamical system; and Random Number Theory

**Lecturer**: Carl Pomerance

**Date**: November 8, 2016

**Main Topics**: Chains with , distribution of primes, randomness in math

**Definitions:** Amicable, Perfect, Abundant, Deficient

Continue reading The first dynamical system; Random Number Theory – Ramsey Doccourse Prague 2016

## Hrushovski constructions – Ramsey DocCourse Prague 2016

**Title**: Hrushovski constructions 1 (of 3)

**Lecturer**: David Evans

**Date**: November 7, 2016

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

**Definitions:** -very-sparse, -orientable,

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

**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

Continue reading Dynamical systems and Ramsey theory – Ramsey DocCourse Prague 2016