Conference: Discovery school: Kahler Geometry, Algebraic and Arithmetic Geometry, Hyperbolicity

This award supports the participation of early-career US-based researchers at the summer school on Kähler Geometry, Algebraic and Arithmetic Geometry, and Hyperbolicity, which will be held from August 24-28, 2026 at the Université du Québec à Montréal in Montreal, Canada. This intensive program provides research training for graduate student and postdoctoral participants, and will foster international collaboration. Kähler geometry is a branch of complex geometry, where functions given by convergent series are particularly well-behaved, in which one has a good notion of distance between points. A fascinating collection of Kähler geometries are hyperbolic—these are curved so much that they cannot contain infinite straight lines. A big source of such geometries comes from algebraic geometry, the study of shapes—called algebraic varieties—defined using only polynomial equations. There are tantalizing questions relating hyperbolicity of algebraic varieties and the arithmetic complexity of their points.

The summer school is distinguished by its integrated focus on Kähler geometry, algebraic and arithmetic geometry, and hyperbolicity, bringing together analytic, topological, and algebraic perspectives within a single coherent program. The program will emphasize developments within the last two decades, including recent analytic methods, such as singular Kähler metrics and complex Monge-Ampère techniques, and their applications. The mini-courses will be delivered by leading scientific experts: Robert Lazarsfeld (Stony Brook University), Hélène Esnault (Freie Universität Berlin, University of Copenhagen), Dan Abramovich (Brown University), Benoît Claudon (Université de Rennes), and Philippe Eyssidieux (Université Grenoble-Alpes). For more information, please see the website for the program: https://ism.uqam.ca/Kahler/en/

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.

Award Number: 2618241
Principal Investigator: Dan Abramovich
Funds Obligated: $19,000
State: RI