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 |