Asymptotically Hyperbolic Manifolds (18w5108)


(University of Alberta)

(Stanford University)

(Uppsala Universitet)


The Banff International Research Station will host the "Asymptotically Hyperbolic Manifolds" workshop from May 13th to May 18th, 2018.

Most of us are familiar with the geometry of Euclid, which is based on the properties of the flat plane. But there are two other similarly fundamental simple geometries and, as Riemann showed, infinitely more if you allow for more complicated, less symmetrical geometric structures. Of the two other most simple geometries, one is the geometry of the sphere, but the other is perhaps less familiar: it's the geometry of the hyperbolic plane, popularized in the work of the artist MC Escher. The subject of this workshop is Riemannian geometries that resemble hyperbolic geometry at large distances. These geometries are called asymptotically hyperbolic (AH) manifolds. Remarkably, these geometries play a fundamental role in modern physics. They appear (with a slight twist) in general relativity, where that are called asymptotically anti-de Sitter spacetimes (AdS). They are fundamental in string theory and particle physics, through what is known as the AdS/CFT correspondence, a paradigm for relating two otherwise very distinct objects, quantum conformal field theory and gravitation. In pure mathematics, AH manifolds have revolutionized our understanding of conformal geometry.

The field has seen spectacular advances in the past 25 years, increasing our understanding of many issues, but also raising many tantalizing new questions. This workshop will bring together experts in the many diverse areas touched by asymptotically hyperbolic manifolds and asymptotically anti-de Sitter spacetimes, to consolidate the advances of the recent past and to focus attention on the most pressing new questions in the field.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).