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Spectrahedra and their geometry

Algebraic Geometry

Speaker: Claus Scheiderer, Universität Konstanz
Related Webpage: http://www.math.uni-konstanz.de/~scheider/
Location: 2112 MSB
Start time: Wed, Mar 20 2019, 1:10PM

A spectrahedron is an affine-linear slice of the cone of positive semidefinite real symmetric matrices. Equivalently, it is the solution set of a linear matrix inequality. Spectrahedra have received much attention since they are the feasible sets of
semidefinite programming. Many problems from a wide range of applications can be phrased as or approximated by a semidefinite program. In my talk I will first give a general introduction to spectrahedra, and then focus on Gram spectrahedra, which arespectrahedra that parametrize the sum-of-squares representations of fixed polynomials.