Title: A toolkit for understanding complete differential varieties.
Abstract: Differential varieties are analogues of algebraic varieties that are defined by differential polynomials instead of algebraic ones. The presence of derivations significantly complicates the study of differential algebraic geometry. As a result, the area has developed a different flavor than its
algebraic counterpart. As an illustration, we discuss the open problem of determining when a differential variety V is complete; i.e., for every differential variety W, the second projection map V × W → W takes closed sets to closed sets. To study this question, we turn to a varied toolkit that includes results from model theory (mathematical logic) as well as computational algebra. The talk will provide the necessary background on these tools, as well as directions for future research into the completeness problem.