Contents/conteúdo

Mathematics Department Técnico Técnico

Summer Lectures in Geometry  RSS

Sessions

27/06/2011, 14:00 — 15:00 — Room P3.10, Mathematics Building
, Massachusetts Institute of Technology

Topological Automorphic Forms

Modular forms and topology

In this survey talk I will describe how modular forms give invariants of manifolds, and how these invariants detect elements of the homotopy groups of spheres. These invariants pass through a cohomology theory of Topological Modular Forms (TMF). I will review the role that K-theory plays in detecting periodic families of elements in the homotopy groups of spheres (the image of the J homomorphism) in terms of denominators of Bernoulli numbers. I will then describe how certain higher families of elements (the divided beta family) are detected by certain congruences between q-expansions of modular forms.

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/Behrenstalk1.pdf

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

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