Description
Gibbs manifolds are images of affine spaces of symmetric matrices under the exponential map. They arise in applications such as optimization, statistics and quantum physics, where they extend the ubiquitous role of toric geometry. The Gibbs variety is the zero locus of all polynomials that vanish on the Gibbs manifold. In this talk, I will describe some properties of this variety, and present two implicitization algorithms (one symbolic and one numerical) for it. In particular, we will see on examples that numerical methods allow to compute more complicated Gibbs varieties. This is based on joint work with Bernd Sturmfels and Simon Telen.
