Edward Witten once said that Elliptic Cohomology was a piece of
21st Century Mathematics that happened to fall into the 20th
Century. He also likened our understanding of it to what we know of
the topography of an archipelago; the peaks are beautiful and
clearly connected to each other, but the exact connections are
buried, as yet invisible. This very active subject has connections
to algebraic topology, theoretical physics, number theory and
algebraic geometry, and all these connections are represented in
the sixteen papers in this volume. A variety of distinct
perspectives are offered, with topics including equivariant complex
elliptic cohomology, the physics of M-theory, the modular
characteristics of vertex operator algebras, and higher chromatic
analogues of elliptic cohomology. This is the first collection of
papers on elliptic cohomology in almost twenty years and gives a
broad picture of the state of the art in this important field of
mathematics.
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