Mathematical Sciences/GIG: Southwest Center for Arithmetical Algebraic Geometry

数学科学/GIG：西南算术代数几何中心

• 批准号: 9709662
• 负责人: Douglas Ulmer
• 金额: $ 50万
• 依托单位: University of Arizona
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-09-01 至 2002-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9709662&HistoricalAwards=false
• 关键词: Mathematical; Sciences; GIG; Southwest; Center

The investigators will establish a Center for Arithmetical Algebraic Geometry at the University of Arizona, in collaboration with the Universities of New Mexico, Southern California, and Texas. The center will further the research of the principal investigators; provide a forum for studying, extending, and disseminating the latest results in arithmetical algebraic geometry and related fields; and enhance the education and professional development of graduate students and recent PhDs in mathematics. Arithmetical algebraic geometry is a field of fundamental research which has its roots in classical problems of arithmetic and geometry, both highly abstract (such as expressing integers as sums of squares) and completely concrete (such as laying out fields for agriculture). On the other hand it has experienced tremendous advances in the twentieth century and is still vitally active today, as evidenced by such heroic advances as Faltings' resolution of the Mordell conjecture and Wiles' proof of Fermat's Last Theorem. Moreover, it has retained its relevance to contemporary life through its connections with robot control, computer vision, RSA data encryption, efficient audio and video compression algorithms, and other aspects of information technology.

研究人员将与新墨西哥州大学、南加州大学和德克萨斯大学合作，在亚利桑那大学建立算术代数几何中心。 中心将进一步推进主要研究者的研究；提供一个研究、扩展和传播算术代数几何及相关领域最新成果的论坛；加强研究生和近期数学博士的教育和专业发展。 算术代数几何是一个基础研究领域，其根源在于算术和几何的经典问题，既高度抽象（例如将整数表示为平方和）又完全具体（例如为农业布局）。另一方面，它在二十世纪经历了巨大的进步，并且在今天仍然非常活跃，法尔廷斯对莫德尔猜想的解决和怀尔斯对费马大定理的证明等英勇的进步就证明了这一点。 此外，它通过与机器人控制、计算机视觉、RSA数据加密、高效音频和视频压缩算法以及信息技术其他方面的联系，保留了与当代生活的相关性。