PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Stephen Simpson.

Title:How nicely can we tweak a nice map?
Seminar:Logic Seminar
Speaker:John Clemens, Pennsylvania State University, University of Muenster
Abstract:
The odometer map is defined on the Cantor space (the space of all infinite sequences of 0's and 1's) by adding 1 (mod 2) with carry to the right. This map has been well-studied and has many nice properties; for instance it admits a simple description as being generated by a finite state automaton. The orbits of the odometer turn out to be equivalence classes of the relation E0 of eventual agreement of sequences, with one exception: the eventually 0 sequences and the eventually 1 sequences comprise a single orbit. We wish to determine how nice a map we can find whose orbits are exactly the E0 classes, i.e., we wish to nicely split the one exceptional orbit of the odometer into two orbits. I will show how we can find a homeomorphism of the Cantor space which generates E0; however, it remains open whether we can find a nicer map, such as an isometry or even one induced by an automaton. I will discuss this question, and how we can eliminate maps with certain additional niceties.

Room Reservation Information

Room Number:MB315
Date:07 / 12 / 2011
Time:09:45am - 11:00am