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Daily Overview |
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RAG2: Real Algebraic Geometry Location: M627 Session Chair: Daniel Plaumann Session Chair: Claus Scheiderer | |
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Wachspress' Conjecture and the Geometry of Polycons Gottfried Wilhelm Leibniz Bibliothek, Germany In 1975, Wachspress introduced the notion of polycons and their adjoint curves. He conjectured that the adjoint of a regular real polycon would never vanish anywhere in the polycon's interior. In this talk we present a counterexample to this conjecture. In establishing this counterexample, some beautiful geometry of the space of (adjoints of) polycons is revealed. it will be shown that adjoint curves satisfy a recursive property expressed in terms of contact curves. We will see how this implies a natural correspondence between equivalence classes of linear determinantal representations of cubic curves, families of polycons bounded by three conics, and their (cubic) adjoint curves. | |
