|Date: Friday, February 26, 2016
Location: 4088 East Hall (3:10 PM to 4:00 PM)
Title: Polynomial degree bounds for matrix semi-invariants
Abstract: Even though the invariant ring for a representation of a reductive group is finitely generated, finding strong bounds for the degrees of generators has proved to be extremely difficult. We focus on the left-right action of SL(n)x SL(n) on m-tuples of n-by-n matrices. We show that invariants of degrees at most n(n-1) define the null cone, and that consequently invariants of degree at most n^6 generate the invariant ring in characteristic 0. If time permits, we shall discuss the ramifications of our bound to algebraic complexity theory, such as a polynomial time algorithm for noncommutative rational identity testing.
This is joint work with Harm Derksen.
Speaker: Visu Makam
Institution: U. Michigan