JAMI Program on Noncommutative Geometry, Arithmetic and Related Topics

约翰霍普金斯大学数学系与日美数学研究所(JAMI)合作，在2008年9月至2009年5月期间组织了一项为期一年的非对易几何、算术及相关主题的课程。自1988年以来，约翰霍普金斯大学数学系与贾米进行了卓有成效的合作，通过基础广泛的数学项目促进了数学研究方面的合作，并促进了数学家之间的总体互动。该计划计划通过组织几个小型课程、系列讲座、研讨会、一本论文集和2009年3月的期末会议，调查与非对易几何、数论和数学物理领域之间丰富的相互联系有关的一些主题。上述领域之间的相互作用是一个相当新的数学领域，在过去的几年里迅速成熟，并产生了非常令人兴奋的结果。在这一点上，组织一个关于这些主题的扩展计划似乎是非常及时的，目的是为了对这一研究领域进行更广泛的探索，并分析最近在非对易几何方面取得的主要进展。考虑到国际和平协会作为一个联合项目所取得的最新进展，在整个计划期间和最后的会议上，将特别注意“非对易几何、黎曼Zeta函数、动机和具有一个元素的场”这一主题。在每周的NCGA研讨会(非对易几何和算术研讨会)和期末会议上，主要重点描述最近出现的将非对易几何中著名的量子统计动力系统(BC系统)、相应的非对易动机(BC内生)和新发展的关于绝对点上的方案的代数几何理论联系起来的联系。NSF资金的直接影响是支持和培训相当数量的初级美国研究人员(初级教师、博士后研究员和研究生)，他们将有机会参与该计划。对初级教师、博士后研究员和研究生的指导和培训是每个JAMI项目的核心部分，帮助这些人建立包括世界领先研究人员在内的网络。为了实现这一目标，国际和平协会招募了一个广泛和多样化的参与者群体，特别关注妇女、少数群体和残疾人。根据最近的几个结果，这些结果揭示了数论和非对易几何领域之间令人惊讶的新联系，PI们预计，这个节目播出的研究将在统一的方法下对这些领域的发展产生重大影响。人们对“非交换算术几何”领域的兴趣迅速增长，导致国际数学联合会最近组织了几次研讨会，这些研讨会促进了理论数学家和物理学家之间的协作工作，并吸引了不同领域数量可观的研究生和年轻研究人员的兴趣。

The Johns Hopkins Mathematics Department jointly with the Japan-U.S. Mathematics Institute (JAMI) organizes a year-long program on Noncommutative Geometry, Arithmetic and Related Topics during the period September 2008-May 2009. The Johns Hopkins Mathematics Department has cooperated fruitfully, since 1988 with JAMI to foster collaboration in mathematical research through broadly based programs in mathematics and to promote in general, interaction among mathematicians. This program plans to investigate, with the organization of several mini-courses, lecture series, seminars, a proceedings book and a final conference on March 2009 a number of topics pertaining to the rich interconnection between the fields of Noncommutative Geometry, Number Theory and Mathematical Physics. The interaction between the aforementioned fields is a quite new area of mathematics, which has matured rapidly in the past few years and has produced very exciting results. It seems very timely at this point to organize an extended program on these topics with the aim to pursue a wider exploration of this area of research and also with the goal to analyze the major advances that have been obtained in Noncommutative Geometry in the recent past. In view of very recent developments obtained as a joint project by the PI's, particular attention will be given, during the whole program and at the final conference, to the topic ``Noncommutative geometry, the Riemann zeta-function, motives and the field with one element.'' In the weekly NCGA seminars (noncommutative geometry and arithmetic seminars) and at the final conference main emphasis will be given to describe the link that has recently emerged connecting a well-known quantum statistical dynamical system in noncommutative geometry (the BC-system), the corresponding noncommutative motive (BC-endomotive) and a newly developed algebraic-geometric theory of schemes over the absolute point.The direct impact of NSF funding is that of supporting and training a significant number of junior U.S. researchers (junior faculty, postdoctoral fellows and graduate students), who will gain the opportunity to participate in the program. Mentoring and training of junior faculty, postdoctoral fellows, and graduate students is a central part of every JAMI program, as is helping these individuals develop networks that include the world's leading researchers. To accomplish this, the PI's have recruited a broad and diverse participant group, paying particular attention to women, minorities, and persons with disabilities. In light of several very recent results, which reveal surprising new connections between the fields of Number Theory and Noncommutative Geometry, the PIs expect that the research broadcast by this program will have a major impact on the development of these fields, under a unified methodology. The rapidly increasing interest in the area of ``Noncommutative Arithmetic Geometry'' has led the PI's to the organization of several recent workshops, which generated collaborative work between theoretical mathematicians and physicists and have attracted the interest of an impressive number of graduate students and young researchers across different fields.