Geometric analysis on asymptotically hyperbolic manifolds (26w5550)

The Banff International Research Station will host the "Geometric analysis on asymptotically hyperbolic manifolds" workshop in Banff from April 12 - 16, 2026.

From the time of Euclid to the modern era, the study of geometry was focused on the properties of flat planes and their generalizations now called vector spaces. But for the past two centuries, geometers have discovered a rich world of other geometries. The most symmetrical of these are the geometry of round spheres and the geometry of hyperbolic spaces. The latter are visualized through the famous woodcuts of the Dutch artist Escher.\\

Hyperbolic spaces and, in particular, a generalization called asymptotically hyperbolic spaces, have in recent decades been the focus of intense mathematical interest. They have surprising applications in the physics of string theory and are important for the study of isolated systems in the theory of general relativity. The closely related de Sitter and anti-de Sitter spaces also arise in the study of cosmology. The purpose of this workshop is to bring together established experts and emerging new talents in the field who study diverse aspects of these fascinating objects. We will discuss some of the remarkable recent developments in the geometric analysis of these spaces, including developments in inverse problems, the various meanings of mass-energy in this setting, the interaction between the mathematical developments and physics, and new ideas to extend the theory beyond the asymptotically hyperbolic setting.