

 Sunday, 9:30 AM 
 On Relative Property (T) and Haagerup's Property 
 Ionut Chifan 
 Vanderbilt University, Nashville, TN 
 Abstract
For a given countable group Γ we consider the following three properties:
1. Γ has an infinite subgroup with relative property (T).
2. The group von Neumann algebra L(Γ) has a diffuse von Neumann subalgebra with relative property (T).
3. Γ does not have Haagerup's property.
It is clear that (1) ⇒ (2) ⇒ (3). We prove that both of the converses are false. This is joint work with Adrian Ioana.

 Slides 


 Saturday, 3:00 PM 
 Villadsen Algebras 
 George A. Elliott 
 University of Toronto, Ontario, Canada 
 Abstract
A brief survey of what is known concerning simple C*algebra inductive limits of matrix algebras over compact metric
spaces of unbounded dimension is given. The first such examples, which could not be obtained using bounded dimension,
were given by Jesper Villadsen in his Ph.D. thesis. The question of extending the known classification result in the case
of bounded dimension (due to Gong, Li, and the speaker) to the case of unbounded dimension is considered. It has been
shown by Andrew Toms that the Cuntz semigroup is needed (in addition to the more usual invariants) to distinguish
algebras in this class. It is not clear what other invariants will be needed.



 Saturday, 4:00 PM 
 Perturbations of E_{0}semigroups 
 Ilan Hirshberg 
 Ben Gurion University, Be'er Sheva, Israel 
 Abstract
An E_{0}semigroup is a oneparameter semigroup of endomorphisms of B(H). We consider families of E_{0}semigroups
parametrized by a compact Hausdorff
space X, with the appropriate continuity requirement. We provide a classification
of such perturbed families in terms of an invariant given by vector bundles over the space X, in the case in which all
E_{0}semigroups in the family are of type I_{n} for a given n.
Joint work with Daniel Markiewicz.



 Saturday, 9:00 AM 
 Diagonals in Fell Algebras 
 Alexander Kumjian 
 University of Nevada, Reno, NV 
 Abstract
We say that a C*algebra A is Fell (or type I_{0}) if it is generated by abelian elements. In this case A is almost a continuous
trace algebra but Â need not be Hausdorff. Such algebras arise naturally in the study of certain dynamical systems. We
prove:
• An abelian C*subalgebra B of a type I_{0} algebra A is a diagonal iff it satisfies the extension property. (i.e. pure
states of B extend uniquely).
• Up to RieffelMorita equivalence (RME) each such A contains a diagonal.
• The twists arising from RME algebras of type I_{0} containing diagonals are equivalent in a natural sense.
This opens the door for a classification of such algebras up to RME.
Joint work with Astrid an Huef and Aidan Sims.

 Slides 


 Saturday, 10:00 AM 
 Morita Transforms of Operator Tensor Algebras 
 Paul S. Muhly 
 University of Iowa, Iowa City, IA 
 Abstract
Suppose that E_{i} is a C*correspondence over the C*algebra A_{i}, i = 1,2. A (strong) Morita equivalence between (A_{1},E_{1})
and (A_{2},E_{2}) is an invertible C*correspondence X from A_{1} to A_{2} such that
E_{1} ⊗_{
A1} X ≅ X ⊗_{
A2} E_{2}. In Proc. London
Math. Soc. 81 (2000), 113168, we showed that a Morita equivalence between (A1,E1) and (A2,E2) induces a strong
Morita equivalence between the corresponding tensor algebras T_{+}(E_{1}) and T_{+}(E_{2}) in the sense of Blecher, Muhly and
Paulsen in the Memoirs of the AMS 143 (2000), no. 681. In this talk we will make precise the sense in which a
strong Morita equivalence between (A1,E1) and (A2,E2) induces an isometry between the space of completely contractive
representations of T_{+}(E_{1}) and the completely contractive representations of T_{+}(E_{2}) and discuss other features of the
representation theory of tensor algebras that are preserved under this notion of Morita equivalence.
Joint work with Baruch Solel.

 Slides 


 Sunday, 4:00 PM 
 The Extended Haagerup Planar Algebra 
 Emily Peters 
 University of New Hampshire, Durham, NH 
 Abstract
The extended Haagerup subfactor was the last unknown item on Haagerup's 1993 list of possible smallindex subfactors.
We construct this subfactor by constructing its associated planar algebra. This nishes the classication of subfactors
with index up to 3 + √2. Our construction works by identifying a planar subalgebra of the graph planar algebra of the
desired principal graph. The challenge is to demonstrate that this planar subalgebra is small enough to be a subfactor
planar algebra, which we accomplish by viewing some of the relations on the subalgebra as substitutes for a braiding
relation.
Joint work with Stephen Bigelow, Scott Morrison and Noah Snyder.

 Slides 


 Sunday, 8:30 AM 
 Cocycle Superrigidity for Gaussian Actions 
 Jesse Peterson 
 Vanderbilt University, Nashville, TN 
 Abstract
I will present a general setting to prove U_{fin}cocycle superrigidity for Gaussian actions in terms of closable derivations on
von Neumann algebras. In this setting I will provide new examples of this phenomenon, extending results of S. Popa. I
will also use a result of K. Schmidt to give a necessary cohomological condition on a group representation in order for the
resulting Gaussian action to be U_{fin}cocycle superrigid. This is joint work with Thomas Sinclair.



 Saturday, 5:00 PM 
 Crossed Products by Free Minimal Actions of Z^{d} on Finite Dimensional Compact Metric Spaces 
 N Christopher Phillips 
 University of Oregon, Eugene, OR 
 Abstract
Let X be a finite dimensional compact metric space, and let h: Z^{d} × X → X be a free minimal action. We describe initial
work towards understanding the structure of the transformation group C*algebra C*(Z^{d},X,h).

 Slides 


 Sunday, 3:00 PM 
 On the Classification of Inductive Limits of II_{1}
Factors with Spectral Gap 
 Sorin Popa 
 University of California, Los Angeles, CA 
 Abstract
We consider II_{1} factors M which can be realized as
inductive limits of subfactors, N_{n} ↑ M, having spectral
gap and satisfying the bicommutant condition (N_{n}'∩M)' ∩
M = N_{n}. Examples are the enveloping algebras associated to nonGamma
subfactors of finite depth, as well as certain crossed product
algebras. We use deformation/rigidity techniques to obtain
classification results for such factors and to calculate Connes'
invariant χ(M).



 Saturday, 8:00 AM 
 Skew Products of Topological Graphs and Noncommutative Duality 
 John Quigg 
 Arizona state University, Tempe, AZ 
 Abstract
For (discrete) directed graphs (and subsequently for higherrank graphs), Raeburn et al developed a satisfying theory of
coverings and fundamental groups. The coverings were closely related to skew products, and the associated C*algebras
turned out to be crossed products by coactions. In joint work with Valentin Deaconu and Steve Kaliszewski, we are (in
the process of) developing a version of this theory for the topological graphs of Katsura. The noncommutative duality
seems to carry over, but since the groups are no longer discrete the coverings become something else.

 Slides 


 Sunday, 8:00 AM 
 Fields of Hilbert Spaces over a Topological Space 
 Leonel Robert 
 York University, Toronto, Ontario, Canada 
 Abstract
A field of Hilbert spaces may be expressed as a supremum of locally trivial vector bundles defined on open subsets of the
base space. This point of view may be exploited to transplant results from the theory of vector bundles to the setting of
fields of Hilbert spaces. For example, one can always embed a field of Hilbert spaces inside another one with sufficiently
larger dimension (depending on the covering dimension of the base space). One can use clutching functions to construct
new fields of Hilbert spaces from old ones. If the base space has dimension at most 3, all the isomorphism classes of fields
of Hilbert spaces may be described in terms of cohomological data. I will talk about these and other results obtained
recently in collaboration with Aaron Tikuisis.



 Saturday, 4:30 PM 
 Classification of *Homomorphisms using the Cuntz Semigroup Functor 
 Luis Santiago 
 Universitat Autonoma de Barcelona, Spain 
 Abstract
We will show how the homomorphisms from the C*algebra of continuous function on a tree to a C*algebra of stable
rank one can be classified by means of the Cuntz functor. In the special case when the tree consists of a single edge we
describe a class of codomain C*algebras  not necessarily of stable rank one  for which this classification holds. We will
also discuss how in certain cases the classification fails. These results are obtained in a joint work with Alin Ciuperca
and George Elliott and in a joint work with Leonel Robert.



 Sunday, 10:00 AM 
 II_{1} Factors with an Exotic MASA 
 Dimitri Shlyakhtenko 
 University of California, LosAngeles, CA 
 Abstract
Using an extension of techniques of Ozawa and Popa, we give an example of a nonamenable strongly solid II_{1} factor M
containing an "exotic" maximal abelian subalgebra A: as an A,Abimodule, L^{2}(M) is neither coarse nor discrete. Thus
we show that there exist II_{1} factors with such property but without Cartan subalgebras. It also follows from Voiculescu's
free entropy results that M is not an interpolated free group factor, yet it is strongly solid and has both the Haagerup
property and the complete metric approximation property.
Joint work with Cyril Houdayer.



 Sunday, 5:00 PM 
 Another qBrauer Algebra and Subfactors 
 Hans Wenzl 
 University of California, San Diego, CA 
 Abstract
We study another qdeformation of Brauer's centralizer algebra. It contains the Hecke algebras of type A as a subalgebra,
where the embedding is determined by certain commuting square conditions. This is motivated by the problem of finding
a rigorous construction of subfactors in connection with twisted loop groups. We also give formulas for indices and relative
commutants of such subfactors.


