Linear Series you can't find on Netflix right now

The notion of linear series (a collection of cuts of a given variety by hyperplanes) is critical in algebraic geometry, where it yields a rich theory in which both classical and modern techniques beautifully come together. In this talk, we will discuss some of the basic tools of this theory, and how they provide us with a better understanding of the geometry of algebraic curves. To that end, a geometric interpretation of the well-known Riemann-Roch theorem for curves will be given and, if time permits, some of the main results of Brill-Noether theory will be briefly surveyed.