6 papers
Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties
Viktoriia Borovik, Hannah Friedman, Serkan HoÅten +1
We study energy minimization problems in quantum chemistry through the lens of computational algebraic geometry. We focus on minimizing the Rayleigh quotient of a Hamiltonian over…
Decomposing conditional independence ideals with hidden variables
Yulia Alexandr, Kristen Dawson, Hannah Friedman +3
We study a family of determinantal ideals whose decompositions encode the structural zeros in conditional independence models with hidden variables. We provide explicit decompositi…
Grassmann and Flag Varieties in Linear Algebra, Optimization, and Statistics: An Algebraic Perspective
Hannah Friedman, Serkan HoÅten
Grassmann and flag varieties lead many lives in pure and applied mathematics. Here we focus on the algebraic complexity of solving various problems in linear algebra and statistics…
Counting Homogeneous Einstein Metrics
Renato G. Bettiol, Hannah Friedman
We present an explicit upper bound on the number of isolated homogeneous Einstein metrics on compact homogeneous spaces whose isotropy representations consist of pairwise inequival…
Homotopy Iterators
Paul Breiding, Taylor Brysiewicz, Hannah Friedman
We introduce the concept of homotopy iterators for performing polynomial homotopy continuation tasks in a memory efficient manner. The main idea is to push forward an iterator for…
Likelihood Geometry of the Squared Grassmannian
Hannah Friedman
We study projection determinantal point processes and their connection to the squared Grassmannian. We prove that the log-likelihood function of this statistical model has $(n - 1)…