Mathematics Colloquia and Seminars

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(click for linkage example)

Roughly speaking, a linkage is a bunch of rods and joints in the plane. We can think about the moduli space of a linkage: the space of all its possible positions. In 2002, Misha Kapovich and John Millson proved that you can get any compact algebraic set—that is, the set of zeroes of a collection of polynomials in any number of variables—is the moduli space of some linkage. This implies (through work of Seifert, Nash, Palais, and Tognoli) that any manifold M is a component of the moduli space of some linkage. In the talk, I will sketch the main ideas of Kapovich and Millson, which are very friendly and geometric.