The University of Arizona

Pentagram map and refactorization

Pentagram map and refactorization

Series: Mathematical Physics and Probability Seminar
Location: Math 402
Presenter: Anton Izosimov, University of Arizona

The pentagram map is an evolution on the space of planar polygons introduced by Richard Schwartz in 1992. The image of a polygon P under this map is the polygon P' whose vertices are the intersection points of consecutive “short” diagonals of P (i.e., diagonals connecting second-nearest vertices). The pentagram map can be viewed as a discrete version of the Boussinesq approximation in fluid dynamics.
 
In the talk, I will explain why this map (as well as its certain multidimensional generalizations) is an integrable system, and what this has to do with the QR algorithm for matrix diagonalization.

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