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A small conference was held in September 1986 to discuss new
applications of elliptic functions and modular forms in algebraic
topology, which had led to the introduction of elliptic genera and
elliptic cohomology. The resulting papers range, fom these topics
through to quantum field theory, with considerable attention to
formal groups, homology and cohomology theories, and circle actions
on spin manifolds. Ed. Witten's rich article on the index of the
Dirac operator in loop space presents a mathematical treatment of
his interpretation of elliptic genera in terms of quantum field
theory. A short introductory article gives an account of the growth
of this area prior to the conference.
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