This volume arises out of the conference sponsored by the Journal of Differential Geometry and held at Harvard University to honor the four mathematicians who founded Index Theory. A large number of geometers gathered for this historic occasion which included numerous tributes and reminiscences which will be published in a separate volume. The four founders of the Index Theory - Michael Atiyah, Raoul Bott, Frederich Hirzebruch, and Isadore Singer - are sources of inspiration, mentors and teachers for the other speakers and participants at the conference. The larger-than-usual size of this volume derives directly from the tremendous respect and admiration for the honorees.
Table of Contents: 1. Projective planes, Severi varieties and spheres - M. Atiyah and J. Berndt 2. Degeneration of Einstein metrics and metrics with special holonomy - J. Cheeger 3. The min-max construction of minimal surfaces - T. H. Colding and C. De Lellis 4. Universal volume bounds in Riemannian manifolds - C. B. Croke and M. Katz 5. A Kawamata-Viehweg vanishing theorem on compact Kahler manifolds - J.-P. Demailly and T. Peternell 6. Moment maps in differential geometry - S. K. Donaldson 7. Local rigidity for cocycles - D. Fisher and G. A. Margulis 8. Einstein metrics, four-manifolds, and differential topology - C. LeBrun 9. Topological quantum field theory for Calabi-Yau threefolds and $G_2$-manifold - N. C. Leung 10. Geometric results in classical minimal surface theory - W. H. Meeks III 11. On global existence of wave maps with critical regularity - A. Nahmod 12. Discreteness of minimal models of Kodaira dimension zero and subvarieties of moduli stacks - E. Viehweg and K. Zuo 13. Geometry of the Weil-Petersson completion of Teichmüller space - S. A. Wolpert
