Mathematical Sciences/GIG: Southwest Center for Arithmetical Algebraic Geometry

研究人员将与新墨西哥大学、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。该中心将进一步加强主要研究人员的研究；为学习、推广和传播算术代数几何及相关领域的最新成果提供论坛；加强数学研究生和新近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，它植根于经典的算术和几何问题，既有高度抽象的问题(如将整数表示为平方和)，也有完全具体的问题(如为农业规划田地)。另一方面，它在20世纪经历了巨大的进步，并在今天仍然非常活跃，如法林斯解决了莫德尔猜想和威尔斯对费马最后定理的证明等英勇的进步就是明证。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的其他方面的联系，保持了与当代生活的相关性。

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.