# Contents

## Idea

Topological automorphic forms are a generalization of topological modular forms: where the latter come with the moduli space of elliptic curves, topological automorphic forms are associated to a given Shimura variety. Moreover, just as topological modular forms refine to the tmf-spectrum representing the corresponding cohomology theory, so every Shimura variety induces a cohomology theory $taf$.

## Properties

### Chromatic pattern

chromatic level $n =$12$\geq 3$
cohomology theory/spectrum $E =$KOTMFTAF
algebraic group$GL_1$$GL_2$$U(1,n-1)$
geometric objectmultiplicative groupelliptic curveShimura variety
FQFTsuperparticleheterotic superstring??

## References

### Lectures

Revised on August 16, 2012 14:09:00 by Urs Schreiber (134.147.24.3)