Transversal and Helly-type theorems in Geometry, Combinatorics and Topology (09w5047)


Imre Bárány (Alfred Renyi Institute)

(University of Calgary)

(City College, City University of New York)

(Universidad Nacional Autónoma de Mexico)

(Universidad Nacional Autónoma de México)


The Banff International Research Station will host the "Transversal and Helly-type theorems in Geometry, Combinatorics and Topology" workshop next week, September 20 - September 25, 2009.

A point, a line, a plane, or its generalization in higher dimensions, a hyperplane, is called a transversal to a family of sets if it intersects every member of a family. Eduard Helly proved in 1913 one of the most celebrated results in geometry that gives conditions for the members of a family of convex objects (with convex boundary and without holes) to have a common point. Helly's theorem gives rise to numerous generalizations and variants, many of which focus on conditions for families of objects to have a common transversal.
The proposed workshop will assemble the key people working in this area, in order to explore recent progress and to help focus on future directions of research in geometric transversal theory.

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).