Mathematical Sciences/GIG: Southwest Center for Arithmetical Algebraic Geometry

研究人员将与新墨西哥州、南加州和得克萨斯州的大学合作，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的主要研究人员;提供一个论坛，学习，扩展和传播的最新成果，在算术代数几何和相关领域;并加强教育和专业发展的研究生和最近的数学博士学位。 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（如将整数表示为平方和）又完全具体（如为农业布局）。另一方面，它在20世纪经历了巨大的进步，今天仍然非常活跃，这一点可以从诸如法尔明斯解决莫德尔猜想和怀尔斯证明费马大定理等伟大的进步中得到证明。 此外，它通过与机器人控制、计算机视觉、RSA数据加密、高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，保留了其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.