Fall 2014

The Geometry of Positive Semidefinite Rank

Wednesday, Dec. 16, 2015 2:30 pm3:00 pm PST

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Calvin Lab

Positive semidefinite rank is a generalization of regular and nonnegative matrix ranks. We are interested in the semialgebraic set and boundaries of the set of matrices of rank at most r and of psd rank at most k, where r and k are small. In particular, we describe the algebraic boundary of this semialgebraic set for r=3 and k=2 and conjecture a characterization of the boundary for r=k+1. I will also explain a geometric version of our conjecture in terms of polytopes and spectrahedral shadows. This talk is based on joint work with Elina Robeva and Richard Z. Robinson.