Owen Sizemore

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Name Owen Sizemore
Member for 3 years
Seen 5 hours ago
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Location UW-Madison
Age 29
I am a grad student postdoc at UCLA University of Wisconsin, Madison studying von Neumann Algebras, particularly classification of II_1 factors and connections with ergodic theory, descriptive set theory, and geometric and measurable group theory.
1d
 awarded ● Nice Question
Jun
12
 comment Double ultrapower of the hyperfinite $II_1$-factor
@Valerio: For the Definition 2.) Don't forget to take the closure.
Jun
11
 comment Are Hyperbolic Groups Residually Amenable
Thanks Jon! Perfect
Jun
11
 comment Are Hyperbolic Groups Residually Amenable
@unknown: In the world of discrete groups;There are amenable groups that are not residually finite, take for example the wreath product $G\wr H$ with $G$ and $H$ amenable and $G$ non-abelian, (in fact there are also infinite and simple ones). As far as non-amenable examples, just take one of the examples above and then take a (direct or free) product with a residually finite non-amenable group (eg. $SL_n(\mathbb{Z})$.
Jun
11
 asked How can I tell if a group is linear?
Jun
11
 asked Are Hyperbolic Groups Residually Amenable
Jun
8
 comment What is the source of this famous Grothendieck quote?
The category of von Neumann Algebras and *-homomorphisms is bad, while von Neumann Algebras with completely positive maps is good. (The first one has basically few interesting morphisms, the second has many)
Jun
1
 comment Is the extension of full free group c^* algebra a group?
@Yemon: Ok, yes. This is almost certainly what is meant.
Jun
1
 comment Is the extension of full free group c^* algebra a group?
Is not a \textit{group}? Or do you mean group $C^*$-algebra. In that case what do you mean? Full? Reduced? Something else? You must be specific here because any separable $C^*$-algebra is generated by some representation of the free group on countably many generators.
May
4
 comment Unbounded metrics on groups
Do you mean $\textit{countable}$ group? Otherwise just take the uncountable product of a discrete group. The result is reasonably nice (ie it's a compact topological group). However, the underlying space is not metrizable.
Apr
29
 awarded ● Yearling
Mar
5
 awarded ● Popular Question
Jan
26
 comment How similar/different are dense subgroups of a compact group.
@Misha: This was basically my motivation. I am familiar with the case of lattices and I was wondering if there was anything similar in this sort of "opposite" situation.
Jan
26
 comment How similar/different are dense subgroups of a compact group.
mmm...seems like my initial thoughts are totally wrong
Jan
26
 asked How similar/different are dense subgroups of a compact group.
Dec
28
 awarded ● Popular Question
Dec
23
 awarded ● Nice Answer