UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

August 29, 2016

939 Evans Hall

3:45PM: Bounds on Projective Dimension and Regularity

Jason McCullough

Is there a bound on the projective dimension (resp. regularity) of homogeneous ideals in polynomial rings solely in terms of the degrees of the generators? Are there meaningful bounds when one assumes the ideals are unmixed? What about prime? I will discuss the status of and relationships between these questions, including joint work with Huneke, Seceleanu and Mantero.

5:00PM: Rees-like Algebras and the Eisenbud-Goto Conjecture

Jason McCullough

Regularity is a measure of the computational complexity of a homogeneous ideal in a polynomial ring. There are examples in which the regularity growth is doubly exponential in terms of the degrees of the generators, but better bounds were conjectured for "nice" ideals. Together with Irena Peeva I discovered a construction that overturns some of the conjectured bounds for "nice" ideals - including the Eisenbud-Goto conjecture. I'll explain the construction and some of its consequences.

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