Speaker: Hannah Friedman (UC Berkeley)
Title: Optimization over Two Embeddings of the Grassmannian
Date: 07.02.2024

Abstract: There are two important embeddings of the Grassmannian as varieties: one via Pluecker coordinates and one via orthogonal projection matrices. While the latter appears more frequently in applied settings, both embeddings are of interest in the context of probability and optimization. After introducing some ideas from algebraic statistics, I will discuss one optimization problem on each of these two embeddings of the Grassmannian. The first is a problem coming from determinantal point processes on a projective variety closely related to the Grassmannian in its Pluecker embedding. This leads us to the maximum likelihood degree of this projective embedding. The second is a reformulation of the eigenvalue problem over orthogonal projection matrices which can be extended to flag varieties. This leads us to the linear optimization degree of this affine embedding.