Conference on Arithmetic Geometry and Algebraic Groups

该奖项为2023年5月24日至28日在夏洛茨维尔的弗吉尼亚大学举行的为期五天的“算术几何和代数群”会议提供资金（网站https://sites.google.com/view/agag-at-uva/home）。会议将重点介绍这些领域的最新进展，并探索新的联系。它将有助于识别算术几何中具有潜在应用于代数群的新问题，并将促进代数群的算术理论在一般领域的发展。会议日程包括50分钟的特邀演讲和20分钟的简短交流，以及海报展示。受邀演讲者的名单包括来自美国、加拿大、智利和法国的数学家，以及来自这些国家和其他国家的早期职业数学家的广泛参与，以及一些在数学中代表性不足的群体的成员。会议的主题将包括不同类型域上的局部-全局原理的各种形式，以及在基域的适当离散赋值集上具有良好约简的代数群的分析。这些问题涉及到代数几何和算术几何中许多问题所涉及的非分枝上同问题的研究。反过来，非分枝上同调的有限性结果（包括最近得到的结果）依赖于代数循环的分析。随着这些被认为是算术几何和代数群理论的“传统”主题，该计划将包括最近发现的Diophantine近似对线性群的应用，这已经导致了一个关于有界生成线性群的老问题的解决，并导致了该领域的进一步发展。该奖项反映了美国国家科学基金会的法定使命，并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，被认为值得支持。

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.