The central theme of this volume is the contemporary mathematics of geometry and physics, but the work also discusses the problem of the secondary structure of proteins, and an overview of arc complexes with proposed applications to macromolecular folding is given. "Woods Hole has played such a vital role in both my mathematical and personal life that it is a great pleasure to see the mathematical tradition of the 1964 meeting resurrected forty years later and, as this volume shows, resurrected with new vigor and hopefully on a regular basis. I therefore consider it a signal honor to have been asked to introduce this volume with a few reminiscences of that meeting forty years ago." Introduction by R Bott (Wolf Prize Winner, 2000).