This is an announcement for the paper "On the complexity of the uniform homeomorphism relation between separable Banach spaces" by Su Gao, Steve Jackson, and Bunyamin Sari. Abstract: We consider the problem of determining the complexity of the uniform homeomorphism relation between separable Banach spaces in the Borel reducibility hierarchy of analytic equivalence relations. We prove that the complete $K_{\sigma}$ equivalence relation is Borel reducible to the uniform homeomorphism relation, and we also determine the possible complexities of the relation when restricted to some small classes of Banach spaces. Moreover, we determine the exact complexity of the local equivalence relation between Banach spaces, namely that it is bireducible with $K_{\sigma}$. Finally, we construct a class of mutually uniformly homeomorphic Banach spaces such that the equality relation of countable sets of real numbers is Borel reducible to the isomorphism relation on the class. Archive classification: math.FA math.LO The source file(s), gjs_24.tex: 107663 bytes, is(are) stored in gzipped form as 0901.4092.gz with size 33kb. The corresponding postcript file has gzipped size 163kb. Submitted from: bunyamin@unt.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0901.4092 or http://arXiv.org/abs/0901.4092 or by email in unzipped form by transmitting an empty message with subject line uget 0901.4092 or in gzipped form by using subject line get 0901.4092 to: math@arXiv.org.