3:45PM: The Size of Free ResolutionsDaniel ErmanLocation: Evans 939The BuchsbaumEisenbudHorrocks rank conjecture roughly says that the Koszul complex is the "smallest possible" free resolution of a graded module. Although BoijSoederberg theory is based on the principle of only considering Betti diagrams up to scalar multiple, I will explain how the structure of BoijSoederberg theory is sufficiently strong to prove new cases of the BuchsbaumEisenbudHorrocks rank conjecture.

5:00PM: Galois Groups of Enumerative ProblemsMorgan BrownTo an enumerative problem, we can associate a Galois group which also acts as the monodromy group on the solutions. This gives vital information about the problem: First it tells us if the solutions are solvable in terms of the original parameters, and second it reflects whether any subset of the solutions have any special configuration. I will present many examples of Joe Harris.
