UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

November 28, 2017

939 Evans Hall

3:45PM: Degree bounds for invariant rings of quivers

Visu Makam

The ring of polynomial invariants for a rational representation of a reductive group is finitely generated. Nevertheless, it remains a difficult task to find a minimal set of generators, or even a bound on their degrees. Combining ideas originating from Hochster, Roberts and Kempf with the study of various ranks associated to linear matrices, we prove "polynomial" bounds for various invariant rings associated to quivers. The polynomiality of our bounds have strong consequences in algebraic complexity, notably a polynomial time algorithm for non-commutative rational identity testing. This is joint work with Derksen.

5:00PM: Complete intersections of given Hilbert polynomial

Chris Eur

The Hilbert polynomial of a homogeneous complete intersection is determined by the degrees of the generators of the defining ideal. The degrees of the generators are not, in general, determined by the Hilbert polynomial but sometimes they are. When? We give some general criteria and completely answer the question up to codimension 6.

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