# Hyperbolicity in the symplectic category (10frg147)

## Organizers

John Bland (University of Toronto)

(University of Notre Dame)

Marianty Ionel (Federal University of Rio de Janeiro)

(University of Houston)

Jens von Bergmann (University of Calgary)

## Description

The Banff International Research Station will host the "Hyperbolicity in the symplectic category" workshop from March 28th to April 4th, 2010.

In the theory of surfaces it is a classical result that they are are determined by it genus. For example, a Riemann surface of genus zero is the sphere, a surface of genus one is a torus, a donut with a single hole, and in general a surface genus $g$ is a donut with $g$ holes. The sphere is said to be rational, a torus is said to be elliptic and a surface of genus $g ge 2$ is said to be hyperbolic. The theory of complex hyperbolic geometry is the study of
higher dimensional complex hyperbolic spaces. In higher dimension we
can no longer visualize spaces so a problem is how one can decide
whether a higher dimensional space is hyperbolic? Geometers introduced
higher dimensional invariants (generalizing the concept of genus for
surfaces) to help settle such questions. The next step is figure out
how we can extend this theory to almost complex spaces -- this is a
much bigger class and the theory is still at its initial stage, much
work needs to be done to answer such questions.

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 US National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnologia (CONACYT).