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

这个奖项为1995年8月在波士顿大学举行的一个名为费马大定理的会议提供了支持。会议将集中讨论两个主要议题：(1)Andrew Wiles最近对半稳定椭圆曲线的谷山-志村-韦尔猜想的证明；(2) Frey、Serre和Ribet的早期工作表明怀尔斯定理将完成费马大定理的证明。会议主要针对高级研究生和刚获得博士学位的学生，但对于寻求掌握证明费马大定理所使用的强大工具的更有经验的数学家来说，它也很有价值。此外，来自波士顿大学PROMYS项目的约80名高中生和本科生将参加更广泛的会议活动，从而增强这些年轻人在PROMYS的经验，并加强数学是一项蓬勃发展的现代研究活动。会议的主题属于算术几何的一般数学领域。这个超现代的研究领域结合了数学的两个最古老的分支：数论和几何。这种结合产生的新见解正在产生越来越强大的工具来解决长期存在的问题，比如费马大定理，它抵制了三个多世纪以来数学家们最强大的努力。此外，虽然算术几何有时被认为是纯数学中最纯粹的，但它也一直在发展富有洞察力的新技术，导致诸如纠错码和密码学等应用领域的巨大进步。

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.