Mathematical Sciences: Workshop on Fermat's Last Theorem; August 9-18, 1995, Boston, Massachusetts

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This award provides support for a conference entitled Fermat's Last Theorem to be held in August 1995 at Boston University. The conference will focus on two major topics: (1) Andrew Wiles' recent proof of the Taniyama-Shimura-Weil conjecture for semistable elliptic curves; and (2) the earlier works of Frey, Serre and Ribet showing that Wiles' Theorem would complete the proof of Fermat's Last Theorem. The conference is aimed primarily at advanced graduate students and recent PhD recipients, but it will also be valuable to more experienced mathematicians seeking to master the powerful tools used in the proof of Fermat's Last Theorem. In addition, about 80 high school students and undergraduates from Boston University's PROMYS program will join the more general conference activities, thereby enhancing these young people's experience in PROMYS and reinforcing that mathematics is a flourishing modern research activity. The themes of the conference belong to the general mathematical area of Arithmetic Geometry. This ultramodern research area combines two of the oldest branches of mathematics: number theory and geometry. The new insights arising out of this combination are producing increasingly powerful tools to solve longstanding problems like Fermat's Last Theorem, which have resisted the strongest efforts of over three centuries of mathematicians. In addition, though Arithmetic Geometry is sometimes regarded as among the purest of pure mathematics, it has also been developing insightful new techniques leading to dramatic progress in such applied areas as error-correcting codes and cryptography.