Series: Penn State Logic Seminar Date: Tuesday, October 23, 2001 Time: 2:30 - 3:45 PM Place: 306 Boucke Building Speaker: Stephen G. Simpson, Mathematics, Penn State Title: New Directions in Descriptive Set Theory Abstract: Let X be a Polish space, and let E be an analytic equivalence relation on X. The space of equivalence classes X/E is known as a singular space. Note that many important non-Polish spaces are singular spaces. For example, the orbit space of a Polish group action on a Polish space is a singular space. An active direction in descriptive set theory is the classification of singular spaces up to mutual Borel embeddability. X/E is said to be Borel embeddable into Y/F if there exists a Borel map f:X-->Y such that, for all x,y in X, xEy iff f(x)Ff(y). This talk is based on the survey paper of the same title by A. Kechris, in the Bulletin of Symbolic Logic, volume 5, 1999, pages 161-174.