# Mathematics Colloquia and Seminars

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### Geometry of orthogonally invariant matrix varieties

**Algebra & Discrete Mathematics**

Speaker: | Dmitriy Drusvyatskiy, Univ. of Washington |

Location: | 1147 MSB |

Start time: | Mon, Apr 11 2016, 4:10PM |

Orthogonally invariant matrix sets – those invariant under left and

right multiplication by orthogonal matrices – appear often in

mathematics. In recent years, an elegant viewpoint has formed: such

sets often inherit algebraic and geometric properties from their

intersections with the subspace of diagonal matrices. Convexity,

smoothness, and algebraicity all follow this paradigm. After surveying

some results of this flavor, I will describe a recent theorem

formalizing the intuition that orthogonally invariant matrix varieties

are in essence no more complicated than their diagonal restrictions.

The two varieties have equal Euclidean distance degrees (an

interesting algebraic complexity measure).

Joint work with Hon-Leung Lee (Washington), Giorgio Ottaviano

(Florence), and Rekha R. Thomas (Washington)