Discrete geometry and topology in low dimensions (07w5111)


(University of Calgary)

(Cornell University)

Herbert Edelsbrunner (Institute of Science and Technology (Austria))


Voronoi cells are widely used in mathematics as well as in many areas of science. Voronoi cells and diagrams can be applied to quite a number of problems and this character of them is a result of the large list of impressive combinatorial, geometric as well as topological properties known today. The workshop hosted at BIRS this week, April 1 – 6, 2007, will focus on some of the most challenging issues on Voronoi cells that are still open today and have the potential to influence significantly the research efforts on many Voronoi cell related applications. In connection with the mathematical theory of Voronoi cells particular emphases will be given to understand the combinatorial, geometric and topological properties of intersections as well as of unions of balls. On one hand, intersections of spherical balls generalize the concept of convex polyhedra fundamental to many parts of today’s science on the other hand, unions of spherical balls not only extend the concept of polyhedra but are highly interesting from the point of view of applications including computational biology when dealing with space-filing diagrams of molecules. This branch of the workshop is connected also to computer science via geometrically motivated data analysis in high dimensional spaces. Among the distinguished conference participants is Professor Stephen Smale (Toyota Technological Institute, Chicago, USA) who won the Fields Medal in 1966 - an international medal awarded once every four years for outstanding discoveries in mathematics. The conference participants represent leading researchers of more than ten countries. This event is co-organized by professors Karoly Bezdek (University of Calgary, Canada), Robert Connelly (Cornell University, USA) and Herbert Edelsbrunner (Duke University, USA).

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 Tecnología (CONACYT).