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# Operator Algebra Seminar

**
Fri., Oct. 6, 2023 2:00 p.m.
**

**
Location: RI 330
**

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

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

*H*,

*K*) II

**Abstract: **

*V*(^{ r}*H*,*K*) was constructed previously. We discuss the manifold further as a quotient space*X*=^{r}*V*(^{r}*H*,*K*)/*U*(*r*) where*U*(*r*) are unitary scalar matrices and construct a probability space (*X*,^{r}*P*). Finally, we show that for every^{ r}*r*= 1, 2, ...,*mn*that*P*{x ∈^{ r}*X*: rank(^{r}*x*) ≠*r*} = 0.