Conference on Arithmetic Geometry and Algebraic Groups

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.