| Talk
Abstracts |
Marius Dadarlat
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E-theory
for C*-algebras over a space. Abstract: We
introduce E-theory for separable C*-algebras over possibly
non-Hausdorff topological spaces and establish its basic properties,
such as six-term exact sequences in each variable and a universality
property. We also plan to discuss certain applications.
(This is joint work with Ralf Meyer).
|
Calder Daenzer
|
A
groupoid approach to orbifold Picard torsors.
Abstract:
I will describe a fairly simple construction with groupoids of
``orbifold Picard torsors.'' These are a common generalization of a
principal bundle, a gerbe, and a family of orbifold groups. I will give
several examples, and show how such objects may be useful in
theoretical physics.
|
Franz Luef
|
Projective
modules over noncommutative tori and Gabor analysis.
Abstract:
In this talk I present an interpretation of projective modules
over noncommutative tori in terms of
Gabor analysis, which is a modern branch of time-frequency analysis.
Furthermore I will discuss spectrally invariant
subalgebras of the noncommutative torus that are different from the
smooth
noncommutative torus and the construction of
projective modules over these spectrally invariant subalgebras. These
results rely on a class of function spaces,
so called modulation spaces. In particular, I will explain the relation
between the modulation spaces and spectrally
invariant subalgebras of the noncommutative torus. Finally I want to
draw
some consequences from this fact about the
structure of Gabor frames, and about the construction of projections in
noncommutative tori.
|
Emily Peters
|
The
extended Haagerup planar algebra.
Abstract:
The extended Haagerup subfactor was the last unknown item on Haagerup's
1993 list of possible small-index subfactors. In recent work with
Stephen Bigelow, Scott Morrison and Noah Snyder we construct this
subfactor by constructing its associated planar algebra. This finishes
the classification of subfactors with index up to $3+\sqrt{2}$. 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.
|
Arlan Ramsay
|
Fourier-Stieltjes
algebras of locally compact groupoids (joint work with
A. Paterson).
|
Jean Renault
|
Cartan
subalgebras in the non Hausdorff case (joint work with
A. Buss and R. Exel). Abstract:
A standard construction associates to a pseudogroup of partial
homeomorphisms of a locally compact Hausdorff space a C$^*$-
algebra. When the groupoid of germs of the pseudogroup is Hausdorff,
the C$^*$-algebra which arises in this fashion can be characterized by
the existence of a nice maximal abelian self-adjoint subalgebra, called
a Cartan subalgebra. More precisely, this construction establishes an
equivalence of categories between twisted \'etale locally compact
Hausdorff effective groupoids and Cartan pairs. This is a
C$^*$-algebraic analogue of a well-known theorem of J.~Feldman and
C.~Moore on Cartan subalgebras in von Neumann algebras. I will report
on the non-Hausdorff case.
|
Sam Schmidt
|
Endomorphisms,
the Toeplitz Algebra and Composition Operators.
Abstract:
Local homeomorphims of the unit circle induce endomorphisms of
the continuous functions on the unit circle, $C(\mathbb{T})$. By
studying
the composition operator associated with certain local homeomophisms
one can
determine when an endomorphism will extend to the Toeplitz algebra,
$\mathcal{T}$. That is, given a local homeomorphism $\sigma: \T
\rightarrow
\T$ when does there exist a $*$-endomorphism $\tilde{\sigma}$ of
$\mathcal{T}$ so that $\tilde{\sigma}(\tau(f) + k) = \tau( f \circ
\sigma) +
k^{\prime}$ where $k^{\prime}$ is some other compact operator? We will
explore this and related questions.
|
| Dimitri Shlyakhtenko |
Strongly
solid II1 factors with
an exotic MASA (joint work with C. Houdayer). Abstract: Using an
extension of techniques of Ozawa and Popa, we give an example of a
non-amenable strongly solid II1factor M
containing an ”exotic” maximal
abelian subalgebra A: as an A,A-bimodule, L2(M)
is neither coarse nor
discrete. Thus we show that there exist II1
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. |
Aidan Sims
|
Algebras
defined by co-universal properties.
Abstract:
In areas such as graph $C^*$-algebras, Cuntz-Pimsner algebras,
crossed product $C^*$-algebras, and $C^*$-algebras of inverse
semigroups, the initial objective is typically
to identify a set of generators and relations which
determine a ``suitable" $C^*$-algebraic realisation of the base
object. The word ``suitable" is used loosely, but is usually
taken to mean that the universal $C^*$-algebra satisfies a
version of the gauge-invariant uniqueness theorem:
every representation which is nonzero on generators and preserves a
canonical gauge-action (typically of $\mathbb{T}$) is
injective.
In this talk we will discuss an approach to formalising the use
of the word ``suitable" using the concept of a co-universal
property inspired by Katsura's work on $C^*$-algebras
associated to Hilbert bimodules. We will discuss some examples
which indicate the advantages of this approach.
This includes joint work with Carlsen, Larsen and Vittadello
and work in progress with Exel and with Brownlowe and
Vittadello.
|
Andrew Toms
|
Ranks of
operators in simple C*-algebras.
Abstract:
Each
(quasi-)trace on a C*-algebra gives rise to a dimension
function---a way of measuring the rank of an operator with respect to
the given trace. The collection of all such then associates to each
operator a function on the trace space. We consider a basic question:
which functions on the trace space arise in this way? We show that the
answer is "all of them, subject to the obvious constraints" for several
classes of simple C*-algebras. These results are then applied to give
Z-stability and classification-by-K-theory results for the algebras
considered. Much of the talk is based on joint work with M. Dadarlat.
|