Graduate seminar on set theory (S4A3)

Organizers

• Prof. Dr. Stefan Geschke
• Dr. Philipp Schlicht

Time and place

Tuesdays 10:00-12:00 at Endenicher Allee 60, room 0.007 .

Contents

Ergodic Ramsey theory uses groMondayup actions to prove combinatorial results, for example about the natural numbers. Notable results in this area include Furstenberg's proof of Szemeredy's theorem that every set of natural numbers of positive upper density contains arbitrarily long (finite) arithmetic sequences, i.e., sequences of the form a, a+d, a+2d, ...

The seminar is based on Stefan Geschke's lecture notes on infinite Ramsey theory and on Randall McCutcheon's Elemental Methods in Ergodic Ramsey Theory (Springer Lecture Notes 1722).

Programme

12 October Marianne Wilms Stone-Čech compactification of discrete spaces

19 October Marianne Wilms Stone-Čech compactification of discrete semigroups

26 October Daniel Schreiber Van der Waerden's theorem

02 November Raimund Fiedler IP-Van der Waerden theorem

09 November Stefan Knauf Hindman's theorem

16 November Allard van Veen Furstenberg correspondence

23 November Allard van Veen Furstenberg correspondence continued

30 November Stefan Geschke Ergodic systems and weak mixing

07 December Stefan Geschke Ergodic systems and weak mixing continued

14 December Thomas Silveira Salles Preparation for Roth's theorem

21 December Thomas Silveira Salles Roth's theorem

11 January Philipp Schlicht Preparation for the Furstenberg structure and recurrence theorems

18 January Philipp Schlicht Furstenberg structure theorem

25 January Stefan Geschke Furstenberg recurrence theorem

01 February Sophie Küster The Ramsey property and the Baire property