Bernd Sturmfels
Max Planck Institute Leipzig, Germany
Gibbs Manifolds
11 September 2023, 5pm
KU Leuven, Department of Electrical Engineering (ESAT) Aula L (ELEC 00.24)
Abstract
Gibbs manifolds are images of linear 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. We compute these polynomials and show that the Gibbs variety is low-dimensional. Our theory is applied to a wide range of scenarios, including matrix pencils and quantum optimal transport. This is joint work with Dmitrii Pavlov and Simon Telen.
