Series: Penn State Logic Seminar Date: Tuesday, February 15, 2005 Time: 2:30 - 3:45 PM Place: 103 Pond Laboratory Speaker: John Clemens, Penn State, Mathematics Title: Fixed Points of Isometries of the Urysohn Space Abstract: A current area of research is investigating the isometry group of Urysohn's universal metric space. In particular, the complexity of classifying isometries up to conjugacy is unknown. I will show that one potential invariant turns out to be very weak in this regard, namely: Given an isometry of Urysohn's space with at least one fixed point, the set of fixed points is in fact isometric to the entire space. I will discuss other possibilities for finding better invariants.