Conference on Arithmetic Geometry and Algebraic Groups

该奖项为2023年5月24-28日在夏洛茨维尔的弗吉尼亚大学举行的为期五天的会议提供资金(网址：https://sites.google.com/view/agag-at-uva/home).会议将突出在这些领域的会场取得的最新进展，并探讨新的联系。这将有助于发现算术几何中可能应用于代数群的新问题，也将促进代数群算术理论在一般领域的发展。大会的节目将包括50分钟的特邀演讲，20分钟的简短交流，以及一次海报会议。被邀请的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的广泛参与，以及一些在数学中未被充分代表的团体的成员。在会议上提出的主题将包括在不同类别的领域上的各种形式的局部-全局原理，以及在适当的基场的离散赋值集合上具有良好约简的代数群的分析。这些问题与未分支上同调的研究有关，它出现在代数几何和算术几何中的许多问题中。反过来，未分枝上同调的有限性结果(包括最近得到的结果)依赖于对代数圈的分析。除了这些被认为是算术几何和代数群理论的“传统”主题外，该计划还将包括最近发现的丢番图逼近在线性群上的应用，这解决了一个关于有界生成的线性群的老问题，并导致了该领域的进一步发展。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.