Syzygies and Compensated Compactness

Linear systems of PDEs can be viewed comprehensively through an algebraic geometric lens. However, most conditions on linear PDEs used in Analysis have a strong Linear Algebra flavor and are difficult to describle using tools of Nonlinear Algebra. We use differential primary decompositions to characterize some of these conditions. In doing so, we prove new properties of the evaluations of polynomial matrices. We aim to use these insights in Analysis applications: weak continuity/lower semicontinuity in Compensated Compactness/Calculus of Variations. Joint work with Marc Härkönen and Lisa Nicklasson.