Advanced topics in mathematical logic - infinite Ramsey theory
- Prof. Dr. Stefan Geschke
Time and place
Tuesdays 12-14 at room 006 and Thursdays 12-14 at room 006.
Very informally, Ramsey's theorem states that an arbitrary structure has large regions that are very simple. We will discuss various aspects infinite (and occasionally finite) Ramsey theory, dealing with continuous colorings (continuous Ramsey theory), Ramsey phenomena in infinite metric spaces and the connections between group and semi-group actions and Ramsey theory. Continuous Ramsey theory has a very set-theoretic flavour,
the group and semigroup acions can be used to prove theorems that are closer to number theory (Furstenberg's proof of Szemeredi's theorem).
More recent developments connect Ramsey theory of classes of finite structure and group actions.
We assume some elementary (!) background in set theory, topology, measure theory and algebra (metric spaces, compactness, Borel sets, Lebesgue measure, groups actions). However, the level of the course will be adjusted to the experience of the audience.