Explore the intricacies of Hilbert polynomials for finitary matroids in this one-hour lecture by Elliot Kaplan from Fields Institute/McMaster University. Delve into topics such as partial differential fields, operators, affinity metroids, and the main theorem. Examine the proof, model theory, and differential difference fields. Investigate the several variable analog and de dilation of convex polyhedra. Gain insights into this complex mathematical subject through a comprehensive exploration of its key concepts and applications.