Lagrangian Grassmannian, equivariant K-theory, compactifications of moduli spaces and other notions from algebraic statistics

The Maximum Likelihood Degree (ML-degree) measures algebraic complexity of a statistical model. This invariant is closely related to the multi-degree of the graph of a gradient map and has been an object of study (under different names) in singularity theory, algebraic geometry, commutative algebra and statistics. Apart from a few cases the formulas for the invariant are not known even in the case of general Gaussian models. Based on a joint work with Monin and Wisniewski, we provide two new approaches to this old problem. Both are related to geometry of the Lagrangian Grassmannian and tori actions. One relates to Schubert calculus and one to Gromov-Witten like invariants.