UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

November 10, 2009

939 Evans Hall


3:45PM: The Size of Free Resolutions

Daniel Erman

Location: Evans 939

The Buchsbaum-Eisenbud-Horrocks rank conjecture roughly says that the Koszul complex is the "smallest possible" free resolution of a graded module. Although Boij-Soederberg theory is based on the principle of only considering Betti diagrams up to scalar multiple, I will explain how the structure of Boij-Soederberg theory is sufficiently strong to prove new cases of the Buchsbaum-Eisenbud-Horrocks rank conjecture.

5:00PM: Galois Groups of Enumerative Problems

Morgan Brown

To 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.

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