Pentagram Map, twenty years after

Description:  Introduced by R. Schwartz more than 20 years ago, the pentagram map acts on plane n-gons, considered up to projective equivalence, by drawing the diagonals that connect second-nearest vertices and taking the new n-gon formed by their intersections. The pentagram map is a discrete completely integrable system whose continuous limit is the Boussinesq equation, a completely integrable PDE of soliton type. In this talk I shall survey recent work on the pentagram map and its generalizations, emphasizing its close ties with the theory of cluster algebras, a new and rapidly developing area with numerous connections to diverse fields of mathematics. In particular, I shall describe a higher-dimensional version of the pentagram map and, somewhat counter-intuitively, its 1-dimensional version. Start Date:  2014-02-12 Start Time:   15:00 Speaker:  Sergei Tabachnikov (Pennsylvania State Univ., USA) Institution:  Pennsylvania State University, Department of Mathematics, USA Place:  Room 2.4 - DMUC URL:  http://www.math.psu.edu/tabachni/ See more:   <Main>