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**: 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].

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