

The 2018 East Coast Operator Algebras Symposium
Texas Christian University
Fort Worth, Texas
October 13 and 14, 2018


Schedule and Abstracts
All talks will take place in Lecture Hall 1 of the Sid
W. Richardson building. See this
map.
Schedule:

Saturday 
Sunday 
99:50 
Jesse Peterson 
Marius Dadarlat 
9:5010:20 
Break 
Break 
10:2010:50 
Kristin Courtney 
Sarah Browne 
11:0011:30 
Bin Gui 
James Gabe 
11:4012:10 
Xin Ma 
END 
12:102:00 
Lunch 

2:002:50 
Rufus Willett 

3:003:30 
Daniel Drimbe 

3:304:00 
Break 

4:004:30 
Rolando de Santiago 

4:405:10 
Corey Jones 

Abstracts:
Titles and abstracts received.
Sarah Browne, Penn State.
Quantitative Etheory
Abstract: Quantitative Etheory is an ongoing project
joint with Nate Brown which aims to create a new approach to
tackling results like the Universal Coefficient Theorem (UCT)
for new classes of C*algebras. In recent years, many people
have been working on classifying C*algebras and these results
assume the UCT, which requires further understanding. The
inspiration is work by OyonoOyonoYu, who used a quantitative
approach of Ktheory to prove the Künneth Theorem for new
classes of C*algebras. An ongoing project of WillettYu extends
the quantitative approach to the KKcontext. Quantitative
Etheory is a generalisation of Etheory and so I will begin my
talk by defining the notion of Etheory and talk about how we
get the definition of Quantitative Etheory. Then I will state
results connecting this definition to Etheory and the UCT.
Kristin Courtney, WWU Münster.
Amalgamated free products of strongly RFD C*algebras over
central subalgebras
Abstract: In 1992, Loring and Exel proved that the unital
full free product of two RFD C*algebras is again RFD. Though
this fails to hold in general for full amalgamated products,
Korchagin showed in 2014 that it does hold when the algebras are
assumed to be separable and commutative. We generalize this
result to pairs of socalled "strongly RFD" C*algebras
amalgamated over a common central subalgebra. Examples of
strongly RFD C*algebras include justinfinite RFD C*algebras,
reduced group C*algebras of virtually abelian groups,
and... what else? This is joint work with Tatiana Shulman.
Marius Dadarlat, Purdue University.
A DixmierDouady theory for strongly selfabsorbing C*algebras
Abstract: The classical DixmierDouady theory classifies
the stable continuous trace C*algebras in terms of the third
cohomology group of their spectra. We plan to give a friendly
introduction to a generalization of the DixmierDouady theory for
continuous fields whose fibers are stable strongly selfabsorbing
C*algebras. An interesting feature of the theory is the appearance
of additional characteristic classes, in higher dimensions. If time
permits, we will discuss the Brauer group in this context.
This is joint work with Ulrich Pennig.
Rolando de Santiago, UCLA.
L\(^2\) Betti numbers of groups and smalleable deformations
Abstract: A major theme in the study of von Neumann
algebras is to investigate which structural aspects of the group
extend to its von Neumann algebra. I present recent progress
made by Dan Hoff, Ben Hayes, Thomas Sinclair and myself in the
case where the group has positive first L\(^2\) Betti number. I
will also expand on our analysis of smalleable deformations and
their relation to cocyles which forms the foundation of our
work.
Daniel Drimbe, University of Regina.
W\(^*\)superrigidity for coinduced actions
Abstract: We prove that if \(\Sigma\) is an amenable
almostmalnormal subgroup of an icc nonamenable group
\(\Gamma\) which is measure equivalent to a product of two
infinite groups, then the coinduced action
\(\Gamma\curvearrowright X\) from an arbitrary probability
measure preserving action \(\Sigma\curvearrowright X_0\) is
W\(^*\)superrigid. In particular, we obtain that any Bernoulli
action of an icc lattice in a product of connected noncompact
semisimple Lie groups is W\(^*\)superrigid.
James Gabe, University of Glasgow.
Traceless AF embeddings and unsuspended Etheory
Abstract: A celebrated theorem of Kirchberg states that
any separable, exact \(C^*\)algebra embeds into the Cuntz algebra
\(\mathcal O_2\). In the same spirit, I have shown that a
separable, exact \(C^*\)algebra embeds into the cone \(C_0((0,1],
\mathcal O_2)\) if and only its primitive ideal space has no
nonempty, compact, open subsets. Consequently, this
characterises when traceless \(C^\ast\)algebras are AF
embeddable, and (under nuclearity assumptions) when Connes and
Higson's \(E\)theory can be unsuspended. The latter result uses
recent results of Dadarlat and Pennig.
Bin Gui, Rutgers University.
Strong commutativity of unbounded operators in 2d conformal field
theory
Abstract: Given two unbounded selfadjoint operators A
and B commuting on a common invariant core of them, the strong
commutatity problem asks if A and B commute strongly, in the
sense that the von Neumann algebras generated by A and by B
commute. This problem has always been important in the
functional analytic approach to quantum field theory. In this
talk, I will discuss this problem in the context of 2d CFT.
Corey Jones, Australian National University.
Generalized crossed products and discrete subfactors
Abstract: We introduce a generalization of the crossed
product construction for C* and von Neumann algebras called the
realization functor. Here, a group action is replaced by an
action of a tensor category together with a connected C*algebra
object internal to that category. We will present the result
that every discrete, extremal, irreducible extension of a
II\(_1\) factor is uniquely characterized as such a crossed
product, and we discuss applications and examples. Based on
joint work with David Penneys.
Xin Ma, Texas A&M.
Title: TBA
Abstract: TBA
Jesse Peterson, Vanderbilt University.
Properly proximal groups and their von Neumann algebras
Abstract: Properly proximal groups and their von Neumann
algebras}{% We introduce a wide class of groups, called properly
proximal, which contains all nonamenable biexact groups, all
nonelementary convergence groups, and all lattices in
noncompact semisimple Lie groups, but excludes all
inneramenable groups. We use properties of these groups to
obtain the first \(W^*\)strong rigidity results for compact
actions of \(SL_d\)(Z) for \(d \geq 3\). This is joint
work with Remi Boutonnet and Adrian Ioana.
Rufus Willett, University of Hawaiʻi at Mānoa.
Property (T) for groupoids
Abstract: Property (T) is a strong rigidity property for
groups: roughly, it says that any representation that is close
to being trivial is actually close to the trivial
representation. Motivated mainly by the problem of constructing
exotic 'Kazhdan projections' in groupoid C*algebras (and the
associated Ktheoretic consequences), I’ll introduce a
topological notion of property (T) for groupoids that
generalizes the group case. This is related to, but in some
ways quite different from, the earlier measuretheoretic notion
of property (T) for groupoids as developed by Zimmer and
AnantharamanDelaroche. I’ll try to explain all this, and also
some other connections and examples. This is based on joint
work with Clément Dell’Aiera.