This workshop explores the mathematics connected to the pentagram map and its generalizations.
With 3 talks per day, spread out over 4 days, leaving time for individualized interactions, it will not be confined to the special topic of the pentagram map, but rather an exploration of the kind of mathematics that it relates to: integrable systems, algebraic dynamics, projective geometry and cluster algebras. The pentagram map is a geometrically flavored dynamical system defined on polygons by a simple and projectively natural straight-line construction. Starting with a polygon, one intersects the shortest diagonals in cyclic order to produce a new polygon with the same number of vertices.
Though quite elementary to define, the pentagram map turns out to have a deep structure connected to completely integrable systems, symplectic geometry, cluster algebras, dimers, algebraic dynamics, and moduli spaces.
The same goes for the many generalizations of the pentagram map, some of which are still quite mysterious.