On the size and shape of betti numbers

Abstract: Given a finitely-generated graded module over a polynomial ring, there are many results and conjectures concerning lower bounds for its betti numbers. Major players in this story include the Syzygy Theorem, the Buchsbaum-Eisenbud-Horrocks Rank Conjecture, and the Total Rank Conjecture. In this talk I'll survey these results and conjectures including a collection of intricately connected recent results that point to even stronger bounds.

commutative algebra

Audience: researchers in the topic

Fellowship of the Ring

Series comments: Description: National Commutative Algebra Seminar

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