Pure Maths Colloquium: Cluster algebras, planar networks, and Integrability of generalized pentagram maps
14 October 2013 16:00 in CM221
This is a joint with M.Gektman, S.Tabachnikov, and A.Vainshtein.
The pentagram map that associates to a projective polygon a
new one formed by intersections of short diagonals was introduced by
R. Schwartz and was shown to be integrable by V. Ovsienko, R. Schwartz
and S. Tabachnikov. M. Glick demonstrated that the pentagram map can
be put into the framework of the theory of cluster algebras.
We extend and generalize Glick's work by including the pentagram map
into a family of discrete completely integrable systems.
In this talk we will discuss our approach to integrability of
pentagram map using cluster algebra.
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