Spectrahedra and their ShadowsAlgebra & Discrete Mathematics
|Speaker:||Bernd Sturmfels, University of California, Berkeley|
|Start time:||Thu, Apr 23 2015, 4:00PM|
This lecture concerns the algebraic geometry that underlies semidefinite programming. After a brief discussion of quartic spectrahedra in 3-space, we focus on spectrahedral shadows, that is, convex sets representable by linear matrix inequalities. We characterize the polynomials that vanish on the boundary of a spectrahedral shadow when the defining matrices are generic. The colorful pictures shown in this lecture can be enjoyed by everyone.