Graduate seminar on set theory (S4A3)
Time and place
Tuesdays 10:00-12:00 at Endenicher Allee 60, room 0.007 .
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).
- 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