Marco Cirant is associate professor of mathematical analysis at the Universit di Padova. F. Reese Harvey is professor emeritus of mathematics at Rice University and the author of Spinors and Calibrations.H. Blaine Lawson is distinguished professor of mathematics at Stony Brook University, a member of the National Academy of Sciences, and the author of six books, including Spin Geometry, with Marie-Louise Michelsohn (Princeton). Kevin R. Payne is associate professor of mathematical analysis at the Universit di Milano and a Fellow of the American Mathematical Society.