Pentagram map, complete integrability and cluster manifolds (10rit139)


Sophie Morier-Genoud (Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie)

Valentin Ovsienko (CNRS, Institut Camille Jordan, Universite Claude Bernard Lyon 1)

(Pennsylvania State University)


The Banff International Research Station will host the "Pentagram map, complete integrability and cluster manifolds" workshop from May 30th to June 6th, 2010.

The pentagram map is a natural operation on polygons. Given an n-gon P, the new n-gon, T(P), is the convex hull of the intersection points of consecutive shortest diagonals of P. The map T exhibits a quasi-periodic behavior and is completely integrable. The dynamics, geometry and algebra of the pentagram map is intimately related with a number of important research areas: discrete differential geometry, completely integrable systems of soliton type, and the theory of cluster algebras. The case of pentagons is classical and goes back to C.-F. Gauss.

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 Tecnolog�a (CONACYT).