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Mathematics Colloquium


Date:  Tuesday, April 02, 2013

Title:  Sumner Myers colloquium: The pentagram map and Y-patterns

Abstract:  The pentagram map is defined by the following construction: given a polygon as input, draw all of its "shortest" diagonals, and output the smaller polygon which they cut out. This operation was introduced by R. Schwartz in the 1990's and has received considerable attention in the past few years within both the discrete integrable system and cluster algebra communities. I will explain how expressing the pentagram map in certain cross ratio coordinates makes it possible to realize the map as a sequence of mutations in a cluster algebra. This connection leads to explicit formulas for the iterates of the pentagram map in terms of generating functions. The underlying combinatorial objects driving the formulas are a family of posets which arose in the work of N. Elkies, G. Kuperberg, M. Larsen, and J. Propp on alternating sign matrices.

Speaker:  Max Glick
Institution:  Univ of Michigan


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