# Mathematics Colloquia and Seminars

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### Semidefinite descriptions of the convex hull of rotation matrices

**Optimization**

Speaker: | Prof. Pablo Parrilo, MIT |

Location: | 3106 MSB |

Start time: | Thu, Nov 6 2014, 11:00AM |

We study the convex hull of SO(n), thought of as the set of n×n orthogonal matrices with unit determinant, from the point of view of semidefinite programming. We show that the convex hull of SO(n) is doubly spectrahedral, i.e. both it and its polar have a description as the intersection of the cone of positive semidefinite matrices with an affine subspace. Our spectrahedral representations are explicit, and are of minimum size, in the sense that there are no smaller spectrahedral representations of these convex bodies. Joint work with James Saunderson and Alan Willsky. Preprint available at arXiv:1403.4914.