Conference: Arakelov and Diophantine Geometry

The workshop on Arakelov geometry and Diophantine geometry is a one week workshop to be held August 3-7, 2026 at Brown University. Following immediately after the International Congress of Mathematicians (ICM) 2026 in Philadelphia, the goal of the workshop is to bring together experts in active and influential branches of arithmetic geometry to initiate conversation and collaboration and to make progress on central problems in number theory. This award will support the travel and accommodation for speakers and participants, with priority given to graduate students, postdoctoral researchers, and early career mathematicians. Information about the conference may be found at the website: https://ziyangjeremygao.github.io/Conference/Brown2026/Brown2026.html Diophantine geometry, that is, the study of rational solutions to polynomial equations has been a central topic of number theory. Many of its major problems, including the Mordell conjecture and the Birch and Swinnerton-Dyer conjecture, have shaped the foundation of arithmetic geometry. Arakelov geometry, the study of intersection theory in an arithmetic setting, has been a powerful tool behind many key breakthroughs in arithmetic geometry. In the past decade, these fields have witnessed significant growth and activity. In particular, tools from these two directions come together in many recent important works, such as the resolution of the Uniform Mordell–Lang Conjecture, the proof of the Unbounded Denominators Conjecture, the study of the Beilinson–Bloch height on algebraic cycles, and the progress towards the Uniform Boundedness Conjecture on rational torsion points of abelian varieties. The state of the art within the subject will be highlighted through 18 plenary talks and 5 shorter talks covering a broad array of topics in Arakelov geometry, Diophantine geometry, and related themes in number theory. 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. NSF Award ID: 2610319 | Program: 01002627DB NSF RESEARCH & RELATED ACTIVIT | Principal Investigator: Nicole Looper | Institution: Brown University, PROVIDENCE, RI | Award Amount: $44,981 View on NSF Award Search: https://www.nsf.gov/awardsearch/show-award/?AWD_ID=2610319 View on Research.gov: https://www.research.gov/awardapi-service/v1/awards/2610319.html