Edward Timko

Date: | Tuesday, November 21, 2017 |
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Time: | 15:00 |

Location: | 205 Armes |

Let \(\mathbb{V}\) denote an \(n\)-tuple of shifts of finite multiplicity, and denote by \(\mathrm{Ann}\:(\mathbb{V})\) the ideal consisting of polynomials \(p\) in \(n\) complex variables such that \(p(\mathbb{V})=0\). If \(\mathbb{W}\) on \(\mathfrak{K}\) is another \(n\)-tuple of shifts of finite multiplicity, and there is a \(\mathbb{W}\)-invariant subspace \(\mathfrak{K}'\) of finite codimension in \(\mathfrak{K}\) so that \(\mathbb{W}|\mathfrak{K}'\) is similar to \(\mathbb{V}\), then we write \(\mathbb{V}\lesssim \mathbb{W}\). If \(\mathbb{W}\lesssim \mathbb{V}\) as well, then we write \(\mathbb{W}\approx \mathbb{V}\).

In the case that \(\mathrm{Ann}\:(\mathbb{V})\) is a prime ideal we show that the equivalence class of \(\mathbb{V}\) is determined by \(\mathrm{Ann}\:(\mathbb{V})\) and a positive integer \(k\). More generally, the equivalence class of \(\mathbb{V}\) is determined by \(\mathrm{Ann}\:(\mathbb{V})\) and an \(m\)-tuple of positive integers, where \(m\) is the number of irreducible components of the zero set of \(\mathrm{Ann}\:(\mathbb{V})\).

Upcoming Seminars

Rings and Modules seminar:

**R. W. Quackenbush**:
*When is a \(\vee\)-semilattice a lattice?*

Tuesday, November 21 at 14:40,
418 Machray Hall.

Functional Analysis seminar:

**Edward Timko**:
*A Classification of \(n\)-tuples of Commuting Isometries*

Tuesday, November 21 at 15:00,
205 Armes.

Geometry and Topology seminar:

**Marc Ethier**

Friday, November 24 at 13:30,
316 Machray Hall.

Combinatorics seminar:

**Anthony Bonato**:
*Burning spiders and path forests*

Friday, November 24 at 15:30,
418 Machray Hall.