Sampling and Data in Algebraic Geometry

The goal of this workshop is to deepen connections between algebraic geometry and data science. Behind many optimization methods is the modeling assumption that data lie on, or close to, an algebraic variety. We will discuss methods to sample from varieties or distributions centered on them, extending the methods to adaptive techniques and for sampling from level sets. We will investigate consequences and applications of these methods for computations in Bayesian statistics, likelihood inference, and topological data analysis. A complementary area of focus will be on learning functions and varieties from samples, and its uses to test goodness of fit, to investigate the geometric and topological structure of data, and for structured matrix and tensor decompositions. The workshop is at the interface of applied algebraic geometry with its applications in numerical computations, machine learning, and statistics. It will bring researchers from these communities together to learn from each other and exchange ideas.