# Mathematics Colloquia and Seminars

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### The toric geometry of triangulated polygons in Euclidean space

**Geometry/Topology**

Speaker: | John Millson, University of Maryland, College Park |

Location: | 2112 MSB |

Start time: | Tue, Nov 20 2012, 3:10PM |

I will talk about the moduli space M of n-gons with fixed side-lengths in Euclidean space, the bending integrable systems on M constructed with Misha Kapovich and a quotient stratified symplectic space M(T) associated to a triangulation T of a reference convex planar n-gon constructed by Kamiya and Yoshida. It was conjectured by Philip Foth and Yi Hu that M(T) was isomorphic to the stratified space underlying the toric fiber of the flat toric degeneration, also depending on T, of M constructed by Speyer and Sturmfels using combinatorial commutative algebra (and no geometry). In my lecture I will explain the proof of this conjecture given by Ben Howard, Chris Manon and me.