Title
"Betti numbers of Graded Moduls and Cohomology tables of Coherent Sheaves"
Abstract:
It can be very difficult to analyze for a given system of polynomials equations
qualitative properties, such as the geometry of the corresponding variety.
The theory of syzygies offers a tool for looking at systems of equations,
which might help to make their subtle properties visible.
In a recent paper Boij and S\"oderberg introduced a series of conjectures, which
characterize all possible syzygy numbers of graded modules over the
polynomial ring up to rational multiples. In the talk, I report on joined work
with David Eisenbud, which proves these conjectures and an analogous statements
for cohomology tables of coherent sheaves.