Time:  3:30pm  4:30 pm 
Room: 
Wean Hall 8220

Speaker: 
Andy Zucker Department of Mathematical Sciences CMU 
Title: 
Topological dynamics and Devlin's theorem

Abstract: 
If G is a topological group, a Gflow is a compact Hausdorff space X with a continuous right action a: X x G to X. A Gambit is just a flow X along with a point x_0 in X whose orbit is dense. After a brief introduction to the world of Gflows and Gambits, we will define a new dynamical object, a completion ambit, and discuss some of their basic properties. Of course, given any category of dynamical systems, it's natural to ask whether the category has a universal object, and if so, if it is unique. Time permitting, we will connect these questions to a striking theorem of D. Devlin from his 1979 thesis about the partition properties of the countable dense linear order. 