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GTC Main Seminar: Spectrahedral Shadows October 24, 2017 (10:00 AM PDT - 11:00 AM PDT)
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Location: MSRI: Simons Auditorium
Speaker(s) Claus Scheiderer (Universität Konstanz)
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A spectrahedron is an affine-linear section of the cone of positive semidefinite matrices. A spectrahedral shadow is a linear image of a spectrahedron. By means of interior point methods one can very effectively optimize linear functions over spectrahedral shadows (semidefinite programming). We will discuss examples and construction methods of spectrahedral shadows, and then turn to the recent disproof of the Helton-Nie conjecture, which stated that every convex semialgebraic set is a spectrahedral shadow. Explicit counter-examples will be given, and a number of related open questions will be addressed.

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