Series: Penn State Logic Seminar Date: Tuesday, September 7, 2004 Time: 2:30 - 3:45 PM Place: 307 Boucke Building Speaker: John Clemens, Penn State, Mathematics Title: Structures With Many Automorphisms Abstract: Descriptive set theory can be used to gauge the complexity of classifying various collections of countable structures up to isomorphism. We generally expect symmetric structures (ones with large automorphism groups) to be easier to classify. In several situations, though, this turns out not to be the case. One example is the theory of graphs, where classifying vertex-transitive graphs up to isomorphism turns out to be just as complicated (in a sense I will make precise) as classifying all graphs up to isomorphism. I will discuss the general theory of classifying countable structures and explain how a result of Mekler allows us to find complexity even among certain symmetric structures.