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# Operator Algebra Seminar

**
Fri., Sep. 22, 2023 2:00 p.m.
**

**
Location: Math/Stat Boardroom CW307.14.3
**

**Speaker: **Shane Crerar, University of Regina

**Title: **Probability of Entanglement: the noncommutative sphere *V ^{ r}*(

*H*,

*K*)

**Abstract: **

The set of isometries from a fixed faithful state of B(H) to a state of *B*(*K* ⊗ *H*) with 2 ≤ dim *H* ≤ dim *K* can be associated with a real-analytic manifold labelled *V ^{ r}*(

*H*,

*K*). The construction of the manifold and its properties will be discussed.

*Z*, the zeroes of real analytic functions from

*V*(

^{ r}*H*,

*K*) to a dimension

*d*real vector space are sets of Lebesgue measure zero when

*Z*is a strict subset of

*V*(

^{ r}*H*,

*K*).