UW Combinatorics and Geometry Seminar: Hannah Friedman

The Grassmannian is studied very differently in pure and applied mathematics. From studying these two embeddings of the Grassmannian, a new variety called the squared Grassmannian arises naturally as the image of the Grassmannian in its Plücker embedding under the coordinate-wise squaring map. We summarize what is known so far about the squared Grassmannian, e.g., dimension, degree, etc. The squared Grassmannian also arises in statistics as the model for a family of probability distributions called projection determinantal point processes. We give an overview of the work that has been done on the likelihood geometry of projection determinantal point processes. Our main result is that the log-likelihood function of this statistical model has  $(n-1)!/2$critical points, all of which are real and positive.