29/06/2011, 14:00 — 15:00 — Sala P3.10, Pavilhão de Matemática
Mark Behrens, MIT
Topological Automorphic Forms
Topological Automorphic Forms II: examples, problems, and applications
I will survey some known computations of Topological Automorphic Forms. K-theory and TMF will be shown to be special cases to TAF. Certain TAF spectra have been identified with by Hill and Lawson, showing these spectra admit ring structures. -local TAF gives instances of the higher real K-theories , one of which shows up in the solution of the Kervaire invariant one problem. Associated to the TAF spectra are certain approximations of the -local sphere, which are expected to see "Greek letter elements" in the same manner that TMF sees the divided beta family. Finally, I will discuss some partial results and questions concerning an automorphic forms valued genus which is supposed to generalize the Witten genus.
- Mark Behrens, Notes on the construction of TMF (2007).
- Mark Behrens and Tyler Lawson, Topological Automorphic Forms, Memoirs of the AMS 958 (2010).
- Paul Goerss, Topological modular forms (after Hopkins, Miller and Lurie), Séminaire Bourbaki, 2009.
- Mike Hopkins, Topological modular forms, the Witten genus and the Theorem of the cube, Proceedings of the 1994 ICM.
- Mike Hopkins, Algebraic Topology and Modular Forms, Proceedings of the 2002 ICM.
- Tyler Lawson, An overview of abelian varieties in homotopy theory (2008).
Doug Ravenel's web page for a seminar on topological automorphic forms contains a comprehensive list of references.