Effective methods for spectrahedra in real and convex algebraic geometry

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Spectrahedra are the feasible sets of semi definite programming and are meanwhile widely recognized as a very versatile geometric structure which forms a central link between (real) algebraic geometry and convex optimization. While recent years have provided tremendous progress in the use of semidefinite programming and spectrahedra in approaching real-algebraic problems of various types, effective handling of spectrahedra is still a rather challenging issue. Building upon the state of the art, the goal of the current project is to advance the understanding and handling of spectrahedra. In particular, we shall explore effective methods for tackling computational problems of amoebas (the logarithmic images of algebraic varieties), spectrahedral approaches and relaxations in real algebraic geometry and optimization of polynomials, spectrahedra and complete positivity, as well as stability issues in handling spectrahedra.