Quebec Mathematical Sciences Colloquium

February 8, 2013 from 16:00 to 18:00 (Montreal/Miami time) On location

Pentagram Map, Twenty Years After

Colloquium presented by Sergei Tabachnikov (Pennsylvania State University)

Introduced by R. Schwartz about 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 field with numerous connections to diverse areas of mathematics.


UQAM, Pav. Sherbrooke, 200, rue Sherbrooke O., room SH-3420