Mathematics Colloquia and Seminars

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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.