Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: Primary Ideals and Differential Equations

Seminar | February 4 | 3:45-4:45 p.m. | 939 Evans Hall

 Bernd Sturmfels, UC Berkeley, MPI Leipzig

 Department of Mathematics

An ideal in a polynomial ring encodes a system of linear partial differential equations with constant coefficients. Primary decomposition organizes the solutions to the PDE. This paper develops a novel structure theory for primary ideals in this context. We characterize primary ideals in terms of PDE, punctual Hilbert schemes, and the join construction, and we present an explicit algorithm for computing Noetherian operators. This is joint work with Yairon Cid-Ruiz and Roser Homs.