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Event Type:

Geometry-Topology Seminar

Date/Time:

Monday, February 27, 2017 - 12:00 to 13:00

Location:

Bexell 207

Local Speaker:

Abstract:

Fix an edge length vector $r=(r_1,\ldots,r_n) \in \mathbb{R}^n_+$, not all $0$. The moduli space $\mathcal{M}_r$ is the space of all $n$-gons in he Euclidean plane with edge lengths $r_1,\ldots,r_n$ modulo orientation preserving isometries of the plane. We'll study the topology of these moduli spaces, particularly focusing on the moduli spaces of quadrilaterals and pentagons. The tool of the day is Morse theory, which we'll develop for the uninitiated attendee. The majority of this talk is taken from Kapovich and Millson's 1995 paper "On the moduli space of polygons in the Euclidean plane."