Mathematics Colloquium

Sergei Tabachnikov


"Pentagram map, twenty years after"

Date: Mon, November 17, 2014
Time: 17:15
Place: Research II Lecture Hall

Abstract: 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 my 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.

The colloquium is preceded by tea from 16:45 in the Resnikoff Mathematics Common Room, Research I, 127.