Departmental Colloquium
Harm Derksen
University of Michigan
Constructive Invariant Theory and Noncommutative Rank
Abstract: If G is a group acting on a vector space V by linear transformations,
then the invariant polynomial functions on V form a ring. In this talk
we will discuss upper bounds for the degrees of generators of this
invariant ring. An example of particular interest is the action of the
group SL_n x SL_n on the space of m-tuples of n x n matrices by
simultaneous left-right multiplication. In this case, Visu Makam and
the speaker recently proved that invariants of degree at most mn^4
generate the invariant ring. We will explore an interesting connection
between this result and the notion of noncommutative rank.
4:15 Tea at 4:15
Friday April 13, 2018 at 3:00 PM in SEO 636