Conference on Arithmetic Geometry and Algebraic Groups

该奖项为为期五天的会议提供资金“算术几何和代数组”在弗吉尼亚大学在夏洛茨维尔期间2023年5月24日至28日举行（网站https：//sites.google.com/view/agag-at-uva/home）。会议将突出这些领域的最新进展，并将探讨新的联系。这将有助于确定新的问题，算术几何有潜在的应用代数群，也将促进发展的算术理论代数群一般领域。会议的程序将包括50分钟的邀请演讲，20分钟的简短交流和海报会议。受邀演讲者名单包括来自美国、加拿大、智利和法国的数学家，来自这些国家和其他国家的早期职业数学家广泛参与，和几个成员的团体代表不足的数学。在会议上提出的主题将包括各种形式的地方-不同类域上的整体原理以及在适当的离散赋值集上具有良好约化的代数群的分析基地这些问题与非分歧上同调的研究有关，它出现在代数和算术几何中的许多问题中。反过来，非分歧上同调的有限性结果（包括最近获得的结果）依赖于代数圈的分析。沿着这些主题，这被认为是“传统”的算术几何和代数群理论，该计划将包括最近发现的应用丢番图逼近线性群，该奖项反映了NSF的法定使命，并被认为值得支持通过使用基金会的知识价值和更广泛的影响审查标准进行评估。

The award provides funding for the five-day conference "Arithmetic Geometry and Algebraic Groups" held at the University of Virginia in Charlottesville during the period May 24-28, 2023 (website https://sites.google.com/view/agag-at-uva/home). The conference will highlight recent advances at the meeting ground of those areas and will explore new connections. It will help to identify new questions in arithmetic geometry that have potential applications to algebraic groups and will also promote the development of the arithmetic theory of algebraic groups over general fields. The program of the conference will consist of 50-minute invited talks, 20-minute short communications, and a poster session. The list of invited speakers includes mathematicians from the US, Canada, Chile, and France, with broad participation of early career mathematicians from these and other countries, and several members of groups underrepresented in mathematics.Topics presented at the conference will include various forms of the local-global principle over different classes of fields and the analysis of algebraic groups having good reduction at an appropriate set of discrete valuations of the base field. These issues are related to the investigation of unramified cohomology, which comes up in many problems in algebraic and arithmetic geometry. In turn, finiteness results for unramified cohomology (including those obtained very recently) rely on the analysis of algebraic cycles. Along with these themes, which are considered "traditional" for arithmetic geometry and the theory of algebraic groups, the program will include recently discovered applications of Diophantine approximation to linear groups, which has resulted in the resolution of an old problem concerning linear groups with bounded generation and has led to further developments in the area.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.