Combinatorics: Thilo Weinert (BGU) "The Ramsey Theory of ordinals and its relation to finitary combinatorics"

Mon, 27/02/201710:30-12:30
Rothberg B220 (CS bldg)
Speaker: Thilo Weinert, BGU
Title: The Ramsey Theory of ordinals and its relation to finitary combinatorics
Ramsey Theory is a branch of mathematics which is often times summed up by the slogan “complete disorder is impossible”. An important branch of finitary Ramsey Theory lies in the determination of Ramsey Numbers. Infinitary Ramsey Theory on the other hand is an important branch of set theory. Whereas the Ramsey Theory of the Uncountable often times features independence phenomena, the Ramsey Theory of the Countably Infinite provides many interesting combinatorial challenges.
We are going to review the state of the art of Ramsey-type results about Countably Infinite Structures focusing on the case of ordinal numbers. Some classical problems in this area is related to extremal problems on finite oriented graphs. We are going to discuss this problem setting, results by the speaker and collaborators as well as open problems.