Elemental Methods in Ergodic Ramsey Theory

Randall McCutcheon (auth.)3540668098, 9783540668091

This book, suitable for graduate students and professional mathematicians alike, didactically introduces methodologies due to Furstenberg and others for attacking problems in chromatic and density Ramsey theory via recurrence in topological dynamics and ergodic theory, respectively. Many standard results are proved, including the classical theorems of van der Waerden, Hindman, and Szemerédi. More importantly, the presentation strives to reflect the extent to which the field has been streamlined since breaking onto the scene around twenty years ago. Potential readers who were previously intrigued by the subject matter but found it daunting may want to give a second look.

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Table of contents :
Introduction….Pages 1-4
Ramsey theory and topological dynamics….Pages 5-39
Infinitary Ramsey theory….Pages 40-77
Density Ramsey theory….Pages 78-110
Three ergodic roth theorems….Pages 111-135
Two Szemerédi theorems….Pages 136-152