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Contributing authors: Michael F. Atiyah, M. V. Berry, Ching-Li Chai, Brian Conrey, Jean-Pierre Demailly, F. T. Farrell, James Glimm, David Harbater, Lizhen Ji, Jürgen Jost, Wolfgang Lück, Dan Marchesin, William H. Meeks III, Peter W. Michor, James S. Milne, Frans Oort, Joaquín Pérez, Bradley Plohr, Herman J. J. te Riele, Michael Rubinstein, Norbert Schappacher, Chi-Wang Shu, Dennis Sullivan, Claire Voisin, Shing-Tung Yau.