Abelian varieties as invariants for Riemannian manifolds
Chris Peters

Witten (and later Moore and Witten) inspired by quantum field theory, have  
suggested how to attach in a canonical fashion a normalized theta-function to 
spin manifolds. What lies behind this is a simple but not very well-known 
construction from linear algebra. I shall present this construction and outline 
how it leads to algebraic tori (=abelian varieties) and also how it relates to 
a construction familiar to algebraic geometers: the Weil intermediate Jacobian.