MPI-MiS Leipzig, Germany

- Algebraic Statistics and Gibbs Manifolds -

Abstract: 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. This lecture gives an introduction to these objects from the perspective of Algebraic Statistics.

References:

1. Pavlov, B.Sturmfels and S.Telen: Gibbs manifolds, arXiv:2211.15490
2. Sturmfels, S.Telen, F-X.Vialard and M.von Renesse: Toric geometry of entropic regularization, arXiv:2202.01571
3. Sullivant: Algebraic statistics. Graduate Studies in Mathematics, 194, American Mathematical Society, Providence, RI, 2018
4. Huh and B.Sturmfels: Likelihood geometry, in Combinatorial Algebraic Geometry (eds. Aldo Conca et al.), Lecture Notes in Mathematics 2108, Springer (2014) 63-117.
5. Geiger, C.Meek and B.Sturmfels: On the toric algebra of graphical models, Annals of Statistics 34 (2006) 1463-1492