Professor Su Gao invites you to attend the doctoral dissertation defense of Rebecca Shi on Wednesday, March 20th at 2:00pm, in GAB 317. Cake and coffee will be served in GAB 472 following the event. "Graev Metrics and Isometry Groups of Polish Ultrametric Spaces" Abstract: We will present results about the computation of the Graev metric on free groups. One of the related results answers an open question of Van Den Dries and Gao. We characterize isometry groups of countable noncompact Heine-Borel Polish ultrametric spaces. We define the notion of generalized trees and establish a correspondence between the isomorphism group of a generalized tree and the isometry group of a Heine-Borel Polish ultrametric space. We then introduce weak inverse limits to capture the characterization of isomorphism groups of generalized trees.