Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: Degree bounds for invariant rings of quivers

Seminar | November 28 | 3:45-4:45 p.m. | 939 Evans Hall

 Visu Makam, University of Michigan

 Department of Mathematics

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.