Commutative algebra of subspace and hyperplane arrangements

Arrangements of linear subspaces have connections with a wealth of mathematical objects in areas as diverse as topology, invariant theory, combinatorics, algebraic geometry, and statistics. Arrangements have also recently played a prominent role in applied mathematics, appearing as key players in data mining and generalized principal component analysis, in the study of the topological complexity of robot motion planning, and in the study of configuration spaces and the Gaudin model of mathematical physics. We give an overview of a number of problems having close connections to commutative algebra and algebraic geometry; the field is very broad so this survey is selective.