Title: Betti Number Maximization and Bounds

Abstract: Think about all ideals with your favorite Hilbert function. What are the largest possible Betti numbers for those ideals? Is there an ideal whose Betti numbers attain maximums? Now, think about your favorite Hilbert polynomial. Let's ask the same questions. These questions have been answered by Bigatti and Hulett (1993) and Caviglia and Murai (2010). We will talk about other, related, families of ideals that we could ask these questions about.