Series: Penn State Logic Seminar

Date: Tuesday, November 30, 2004

Time: 2:30 - 3:45 PM

Place: 307 Boucke Building

Speaker: John Clemens, Penn State, Mathematics

Title: Classifying ultrahomogeneous metric spaces


  A metric space is said to be ultrahomogeneous if any partial
  isometry between finite subsets can be extended to an isometry of
  the whole space.  We consider the difficulty of classifying
  separable, complete ultrahomogeneous metric spaces up to
  isometry. On the one hand, the collection of isometry types of
  finite subsets of such a space is a complete isometry invariant
  among these spaces; however, these collections are quite complicated
  objects. We will show that certain types of invariants are not
  sufficient to classify these spaces up to isomtery, in particular
  the isometry relation on ultrahomogeneous spaces does not admit
  classification by countable structures.