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

Lecturer: Carl Pomerance

Date: November 8, 2016

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

Definitions: Amicable, Perfect, Abundant, Deficient

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

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