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Tuesday, December 6, 2005

**Abstract:** This talk will be on joint work with Mark Behrens. We will introduce a recent theorem of J. Lurie which generalizes the Goerss-Hopkins-Miller theorem to some even periodic cohomology theories with associated 1-dimensional p-divisible groups rather than merely formal groups. We will discuss some examples studied by Harris and Taylor in their work on the local Langlands correspondence; the ring spectra associated to these could be regarded as higher chromatic analogs of the topological modular forms spectrum TMF. We close with some discussion of how these might be used to give some computational information about the K(n)-local sphere.