Contents/conteúdo

Mathematics Department Técnico Técnico

Summer Lectures in Geometry  RSS

Sessions

29/06/2011, 14:00 — 15:00 — Room P3.10, Mathematics Building
, Massachusetts Institute of Technology

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 $BP\langle 2\rangle$ 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

https://www.math.tecnico.ulisboa.pt/~ggranja/SummerLect11_files/Behrenstalk3.pdf

For detailed overviews of each course see https://camgsd.tecnico.ulisboa.pt/encontros/slg/.

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