Preface

Summary

A workshop entitled “Elliptic Cohomology and Chromatic Phenomena” was held at the Isaac Newton Institute for Mathematical Sciences in Cambridge, UK, on 9–20 December, 2002. The workshop attracted over 75 participants from thirteen nations. The event, an EU Workshop, was the final one in INI's program New Contexts for Stable Homotopy Theory held in the fall of that year. During the first week nineteen talks described a wide range of perspectives on elliptic genera and elliptic cohomology, including homotopy theory, vertex operator algebras, 2-vector spaces, and open string theories. The second week featured ten talks with a more specifically homotopy theoretic focus, but encompassing the higher chromatic variants of elliptic cohomology.

This was the first conference on elliptic cohomology since the one organized by Peter Landweber at the Institute for Advanced Study in Princeton in 1986. The proceedings of that conference were published in. The breadth of that volume is an indication of the multifaceted nature of the subject. From the start it has provided a meeting point for algebraic topology, number theory, and theoretical physics, playing in the present era a role analogous to the role of K-theory in the second half of the last century. Landweber's introduction to that volume, together with Serge Ochanine's contribution to it, provide good introduction to the origins of this subject.

The starting point was the study of genera of spin manifolds. A genus is a multiplicative bordism invariant, with values in some commutative ring.