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Summer Lectures in Geometry   RSS

29/06/2011, 14:00 — 15:00 — Room P3.10, Mathematics Building
, 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 BP2 by Hill and Lawson, showing these spectra admit E oo ring structures. K(n)-local TAF gives instances of the higher real K-theories EO n, one of which shows up in the solution of the Kervaire invariant one problem. Associated to the TAF spectra are certain approximations of the K(n)-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.

References

Doug Ravenel's web page for a seminar on topological automorphic forms contains a comprehensive list of references.

See also

http://www.math.ist.utl.pt/~ggranja/SummerLect11_files/Behrenstalk3.pdf

For detailed overviews of each course see http://camgsd.ist.utl.pt/encontros/slg/.

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