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.

调查人员将与新墨西哥州，南加州和德克萨斯大学合作，在亚利桑那大学建立一个算术代数几何中心。 该中心将进一步研究主要研究人员；提供一个论坛，用于研究，扩展和传播算术代数几何和相关领域的最新结果；并增强研究生的教育和专业发展以及数学的最新博士学位。 算术代数几何形状是一个基本研究领域，它源于算术和几何学的经典问题，既高度抽象（例如表达整数作为正方形总和）和完全混凝土（例如为农业铺设领域）。另一方面，它在20世纪已经取得了巨大的进步，并且在今天仍然活跃，这是诸如Faltings对Mordell猜想的决议和Wiles'Fermat的最后定理的证据所证明的那样。 此外，它通过与机器人控制，计算机视觉，RSA数据加密，有效的音频和视频压缩算法以及信息技术的其他方面的联系，保留了与当代生活的相关性。