What is... Ramsey Theory?

This page hosts information on Tuan Tran's talk "What is … Ramsey Theory?" at the "What is …?" seminar. The talk will take place on Friday, July 10, 1:00pm at BMS Loft/Urania.

Abstract

Ramsey theory refers to a branch of mathematics whose underlying philosophy is captured by the statement that "Every large system contains a large well-organized subsystem." There are examples of such statements in many areas, including geometry, number theory and analysis.

In this talk, we shall discuss some examples and focus on Roth's theorem, which guarantees that every set of integer with positive density contains a 3-term arithmetic progression. No prior knowledge of combinatorics and number theory is assumed.

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