### Mathematics Colloquium

# Sergei Tabachnikov

### (ICERM)

## "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.*