## Geometry Seminar - Abstracts

### Talk

Thursday 23 February 2017, 16:00 - 17:00 in HG03.085

**Harm Derksen** (University of Michigan, Ann Arbor)

*Matrix Invariants*

### Abstract

The determinant of an n x n matrix is an invariant polynomial of degree n
that is invariant under left and right multiplication with matrices in
SL(n). It generates in the sense that every other invariant polynomial is a
polynomial expression in the determinant. In this talk we consider the
simultaneous left and right action of SL(n) on m-tuples of n x n matrices.
I will explain a joint result with Visu Makam that shows that invariants of
degree at most n^6 are sufficient to generate all polynomial
invariants. These results have applications in Algebraic Complexity Theory.

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