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Title:
Algebraic Geometry and Combinatorics of polygon spaces
Speaker:
Abstract:
From the perspective of algebraic geometry, Moduli spaces of euclidean polygons are known as classical spaces from invariant theory, the moduli spaces of weighted point arrangements on the projective line. I will give a description of the construction of these spaces by Geometric Invariant Theory (GIT) in to ways: as a quotient of a product of projective lines, and as a quotient of the Grassmannian variety of 2-planes. Then I will describe some of the combinatorial gadgets inherited by polygon spaces from these quotient constructions, and how they can be used to draw conclusions about the geometry of polygons. In particular I will describe how the diagonal length polytopes can be derived from this perspective. Along the way I will describe how these algebraic and combinatorial techniques can be applied to other moduli spaces from algebraic geometry.
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