Speaker 
Title and Abstract 
Paul Baum
Pennsylvania State University 
Exact crossed products: a counterexample revisited
The left side of BC (BaumConnes) with coefficients “sees”
any group as if the group were exact. This talk will indicate how to
make a change in the right side of BC with coefficients so that the
right side also “sees” any group as if the group were exact.
This corrected form of BC with coefficients uses the unique minimal
exact intermediate crossedproduct. For exact groups (i.e., all groups
except the Gromov group) there is no change in BC with coefficients.
In the corrected form of BC with coefficients the Gromov group acting
on the coefficient algebra obtained from an expander is not a counterexample.
Thus at the present time (June, 2013) there is no known counterexample
to the corrected form of BC with coefficients. The above is joint work
with E. Kirchberg and R. Willett. This work is based on — and inspired
by — a result of R. Willett and G. Yu.

Bruce Blackadar
University of Nevada, Reno 
Dimension theory for C*algebras
We will survey the various noncommutative versions of dimension
for C*algebras and their applications, beginning with Rieffel's stable
rank. Other dimension theories include real rank, tracial rank, decomposition
rank, and nuclear dimension, all of which have different applications.
Uses of these theories in the structure of approximately homogeneous
C*algebras will be discussed, including approximate divisibility and
Zstability. Finally, we discuss stability questions, the Cuntz semigroup,
and radius of comparison.

Branimir Čačić
Cal Tech 
Towards a reconstruction theorem for toric noncommutative manifolds
A toric noncommutative manifold is a spectral triple obtained
from a commutative spectral triple by applying Rieffel's strict deformation
quantisation to its algebra. We discuss work in progress towards extending
Connes' reconstruction theorem for commutative spectral triples to a
reconstruction theorem for toric noncommutative manifolds.

Alan Carey
Australian National University
Lecture Notes

Scattering theory and Noncommutative Geometry
This talk outlines work in progress on connections between
index theory and scattering theory.

Heath Emerson
University of Victoria
Lecture Notes

Ktheory and the Lefschetz fixedpoint formula
We describe a generalization of the Lefschetz fixedpoint
formula. The formula equates two invariants of a smooth, Gequivariant
selfcorrespondence of a smooth compact manifold, where G is a compact
group. As in the classical formula, one of our invariants is local and
geometric and is based on a selfintersection construction, and the
other is global and homological, and depends, roughly speaking, only
on the R(G)module trace of the R(G)module map on equivariant Ktheory
induced by the correspondence.

Philip Green
University of Washington 
Math vs. Biology
I will discuss my scientific journey from being a student
of Marc Rieffel to working on genomics, and lessons learned along the
way.

Marco Gualtieri
University of Toronto

The Stokes Groupoids
We construct and describe a family of groupoids over complex
curves which serve as the universal domains of definition for solutions
to linear ordinary differential equations with singularities. As a consequence,
we obtain a direct, functorial method for resumming formal solutions
to such equations.

Nigel Higson
Pennsylvania State University 
Noncommutative Geometry of Parabolic Induction and Parabolic Restriction
In his influential work from the 1970s, Marc Rieffel explained
how unitary induction can be neatly framed within ${C^*}$algebras by
using Hilbert modules and the concept of Morita equivalence. In the
last several years, Pierre Clare has begun to study parabolic induction,
which is the mainstay of HarishChandrastyle representation theory,
from the same ${C^*}$algebraic point of view. I shall introduce Pierre’s
basic construction, and then consider the problem of framing “parabolic
restriction” within ${C^*}$algebra theory. For tempered representations
— roughly speaking, for the reduced rather than the full group
${C^*}$algebra — one can expect adjunction relations between parabolic
induction and restriction. The investigation of these relations leads
to some interesting asymptotic geometry — for SL(2,${\mathbb{R}}$)
this is the geometry of the wave equation on the hyperbolic plane. An
asyet poorly understood issue is that the constructions involve the
smooth structure of the tempered dual, as captured by a smooth subalgebra,
and not just the topology, as captured by the reduced ${C^*}$algebra.

Richard Kadison
University of Pennsylvania 
Foundations of the Theory of Murrayvon Neumann Algebras
F. J. Murray and J. von Neumann introduced the family of
unbounded, closed, denselydefined operators that are closely associated
(“affiliated” as they termed them) with a finite von Neumann
algebra. They proved that they have remarkable common, dense domain
properties and described surprising addition and multiplication operations
for them. Zhe Liu and the speaker have defined algebras based on these
operations, Murrayvon Neumann algebras, and studied their basic structure.
This will be discussed during the lecture with special emphasis on the
nature of the derivations of these algebras.

Max Karoubi
Université Paris 7

Algebraic and Hermitian Ktheory of stable algebras
This is joint work with Mariusz Wodzicki. It was conjectured
in 1978 that algebraic Ktheory and topological Ktheory coincide on
the category of stable complex ${C^*}$algebras. This conjecture was
proved by Suslin and Wodzicki about 20 years ago. In this lecture we
give another proof of the conjecture which may be applied to stable
real ${C^*}$algebras or Banach algebras like the algebra of compact
operators in a separable real Hilbert space. We apply our new method
to compute also Hermitian Ktheory of a large class of operator algebras
by a comparison theorem involving the topological analog.

Paweł Kasprzak University
of Warsaw 
Rieffel deformation via crossed products
The aim of this talk is to present a description of the Rieffel
deformation in the crossed product terms. The starting point of our
construction is an action of an abelian group G on a C*algebra A. The
crossed product algebra of A by the action of G is canonically equipped
with the dual action of the dual group of G. The algebra A can be embedded
into this crossed product and it is characterized by the Landstad conditions,
one of which is the invariance with respect to the dual action. Using
a 2cocycle on the dual group one can deform the dual action and the
Rieffel deformation of A is defined as the Landstad algebra for this
deformed dual action. A particular benefits of our approach are immediate
proofs of invariance of Kgroups and preservation of nuclearity under
the Rieffel deformation.

Alan Lai
California Institute of Technology 
Toward understanding the space of connections
What do people mean when they integrate over a large space
like the connection space? Inspired by the formal definition of a path
integral, I attempt to give an interpretation on a measure of the
connection space in loop quantum gravity literature. I will end with
a natural way of interpreting a connection as an operator on a Hilbert
space.

Franz Luef
UC Berkeley
Lectures Notes

Noncommutative geometry and timefrequency analysis
In this talk I describe a link between projective modules
over noncommutative tori and timefrequency analysis, where they are
known as Gabor frames and are of relevance in wireless communication.
The main focus will be on properties of Gabor frames that follow from
the existence of Hermitian connections on projective modules over noncommutative
tori.

Zhiqiang Li
University of Toronto
Lecture Notes

KKlifting problem and order structure on Kgroups
We investigate the KKlifting problem for ${C^*}$algebras,
namely, the problem which KKclass is representable by a *homomorphism
between the algebras (allowing the tensor product with a matrix algebra
for the codomain algebra). This problem not only makes sense in its
own right, but also has application to the classification of ${C^*}$algebras.
To be more precise, we look at this problem for dimension drop interval
algebras (with possibly different dimension drops at the endpoints).
It turns out that there exist KKelements between two such algebras
which preserve the DadarlatLoring order on Ktheory with coefficients,
but can not be lifted to a *homomorphism between the algebras. This
is different from the equal dimension drop case, as shown by S. Eilers.This
is a joint work with George A. Elliott.

Snigdhayan Mahanta
University of Muenster 
Bivariant theories for C*algebras
Bivariant theories are two variable theories which provide
an axiomatic framework to study Etheory and (local) cyclic homology
theory amongst others. One fundamental example of such a theory is noncommutative
stable homotopy, which has received much less attention in the literature.
It is a sharper invariant than Etheory (or KKtheory for nuclear C*algebras)
and hence deserves a closer look. Standard constructions view them as
Homgroups of certain triangulated categories. I will demonstrate that
they have a higher categorical origin and the noncommutative stable
homotopy groups are simply the ordinary homotopy groups of this higher
category. This construction will be applied to address some questions
on the global aspects of noncommutative stable homotopy.

Luis Santiago Moreno
University of Oregon 
Classification of actions of finite abelian groups on AIalgebras
In this talk, I will introduce an equivariant version of the
Cuntz semigroup. Then I will discuss some of its properties. I will
show that if G is a compact group then the equivariant Cuntz semigroup
of a G${C^*}$algebra is naturally isomorphic to the Cuntz semigroup
of the associated crossed product ${C^*}$algebra. I will also explain
how this semigroup can be used to classify actions of finite abelian
groups on AIalgebras with the Rokhlin property. This is a joint work
with Eusebio Gardella.

Sergey Neshveyev
University of Oslo 
Cocycle deformation of operator algebras
Given a ${C^*}$algebra A with an action of a locally compact
quantum group G on it and a unitary 2cocycle ${\Omega}$ on ${\hat{G}}$,
we define a deformation ${A_\Omega}$ of A. We will be particularly interested
in the cases when G is either a genuine group or a group dual. The construction
behaves well under the regularity assumption on ${\Omega}$, meaning
that ${C_0 (G)_\Omega \rtimes G}$ is isomorphic to the algebra of compact
operators on some Hilbert space. In particular, then ${A_\Omega}$ is
stably isomorphic to the iterated twisted crossed product ${G^{op}\rtimes_\Omega
G \rtimes A}$. Also, in good situations, the ${C^*}$algebra ${A_\Omega}$
carries a left action of the deformed quantum group ${G_\Omega}$ and
we have an isomorphism ${G_\Omega \rtimes A_\Omega \cong G \rtimes A}$.
As examples we consider Rieffel’s deformation and deformations
by cocycles on the duals of some solvable Lie groups recently constructed
by Bieliavsky and Gayral. (Joint work with J. Bhowmick, L. Tuset and
A. Sangha.)

Mira Peterka
University of Kansas 
Complex Vector Bundles over HigherDimensional ConnesLandi Spheres
We classify and construct (up to isomorphism) all finitelygenerated
projective modules over higherdimensional ConnesLandi spheres for
totally irrational values of the deformation parameter.

Judith Packer
University of Colorado, Boulder 
Projective multiresolution
analyses: origins and recent developments
In January 1997, Marc Rieffel gave a talk at a special session of
the Joint Annual Meetings entitled “Multiwavelets and operator
algebras”, which related wavelet theory to the Ktheory of the
(commutative) torus. Rieffel’s talk related the multiresolution
analysis theory of wavelets due to S. Mallat and Y.Meyer to a nested
sequence of Hilbert modules over continuous functions on the torus,
and the theory of projective multiresolution analyses had its origins
here. The talk today will relate some of this theory, as well as discussing
some recent developments due to B. Purkis of the University of Colorado,
Boulder.

Bahram Rangipour
University of New Brunswick 
The twisted local index formula is primary
In this talk we introduce a new Hopf algebra with a characteristic
map that captures the twisted local index formula on the groupoid action
algebra. In contrast with the ConnesMoscovici Hopf algebra the cohomology
of this new
Hopf algebra is comprised of all universal Chern classes. This proves
that the cyclic cohomology class of the twisted index cocycle is primary.
The talk is based on the collaboration with Henri Moscovici.

Marc Rieffel
University of California, Berkeley 
Noncommutative resistance networks
To avoid the technicalities of unbounded operators and their
dense domains, in this talk I will deal only with finitedimensional
C*algebras. I will introduce what I am calling a Riemannian metric
over such an algebra A. When A is commutative I will indicate how we
essentially obtain a (finite) resistance network. I will describe interesting
noncommutative examples. In particular, in our setting every spectral
triple determines a Riemannian metric. I will sketch how from a Riemannian
metric we obtain further interesting structures, such as Laplace operators,
seminorms equipping A with the structure of a quantum metric space,
and corresponding metrics on the state space. These seminorms have surprisingly
strong properties. I will also mention how this setup is closely related
to Dirichlet forms and quantum semigroups.

Albert Sheu
University of Kansas 
The structure of quantum line bundles
over quantum teardrops
Over the quantum weighted 1dimensional complex projective
spaces, called quantum teardrops, the quantum line bundles associated
with the quantum principal U(1)bundles introduced and studied by Brzezinski
and Fairfax are explicitly identified among the finitely generated projective
modules which are classified up to isomorphism.

Adam Skalski
Polish Academy of Sciences / University of Warsaw 
Spectral triples on crossed products by equicontinuous actions
I will discuss a method of constructing spectral triples on
crossed products by actions of discrete groups, inspired by the Kasparov
product. A sufficient condition for the method to work, introduced by
Jean Belissard, Mathilde Marcolli and Kamran Reihani for actions of
Z, turns out to be closely related with the topological equicontinuity
of the action, if only the original triple is Lipschitz regular (in
the sense of Rieffel). I will also present certain examples and further
related problems. (Joint work with Andrew Hawkins, Stuart White and
Joachim Zacharias.)

Piotr M. Sołtan University
of Warsaw 
Embeddable quantum homogeneous spaces
I will review some aspect of the theory of noncommutative
(or quantum) homogeneous spaces and describe a natural class of such
objects which in joint work with P. Kasprzak we called "embeddable"
following the original use of this term by Podleś. Along the way
I will devote some attention to a von Neumann algebraic version of this
theory which exhibits an interesting duality. As an example I will shed
some light on the concept of the diagonal subgroup of the direct product
of a quantum group with itself.

Karen Strung University
of Muenster 
On the classification of C*algebras
of minimal dynamical systems of a product of the Cantor set and an odd
dimensional sphere
Let : ${\beta: S^n \rightarrow S^n}$ be one of the known examples
of minimal dynamical systems of n dimensional spheres, n ${\geq}$
3 odd. For every such (${\beta; S^n}$), there is a Cantor minimal
system (X; ${\alpha}$) such that the product system (${X \times S^n;
\alpha \times \beta}$) is minimal and such that tracial state space
of ${C(S^n) \rtimes_ \beta \mathbb{Z}}$ is preserved in ${C(X \times
S^n) \rtimes_{\alpha \times \beta}\mathbb{Z}}$.
I show that ${C(X \times S^n) \rtimes_{\alpha\times\beta}\mathbb{Z}}$
is a tracially approximately interval (TAI) algebra and hence classifiable.
Moreover, with forthcoming work of Wilhelm Winter this implies that
${C(Y ) \rtimes_\beta\mathbb{Z}}$ is TAI after tensoring with the
universal UHF algebra, showing that such crossed products are classified
by their tracial state spaces, as conjectured by N. Christopher Phillips.

Xiang Tang
Washington University 
Equivariant quantization and Ktheory
In the early 90s, Marc Rieffel proved that Kgroups of ${C^*}$algebras
are invariant under strict deformations. In this talk, we will explain
a generalization of this theorem to the equivariant setting. As an application,
this result allows us to compute Kgroups of some noncommutative orbifold
algebras. (Joint work with Yijun Yao).

Andreas Thom
Universität Leipzig

Entropy, Determinants, and ${L^2}$Torsion
This talk is about the entropy of group actions of amenable
groups. I will present recent progress on questions asked by Christopher
Deninger about the entropy of certain principal algebraic dynamical
systems. I will show that the entropy of an algebraic dynamical system
agrees with the ${L^2}$torsion of the dual module over the integral
group ring of the group acting. As a byproduct we prove vanishing of
the ${L^2}$torsion of amenable groups, which was conjectured by Wolfgang
Luck. This is joint work with Hanfeng Li.

Alfons Van Daele
University of Leuven, Belgium
Lecture Slides

The LarsonSweedler theorem and the operator algebra approach to
quantum groups
The LarsonSweedler theorem says that a bialgebra is a Hopf
algebra if there exist a left and a right integral. More precisely,
let A be a unital algebra (say over the field of complex numbers) with
a coproduct ${\Delta : A \rightarrow A \bigotimes A}$ and a counit ${\varepsilon
: A \rightarrow \mathbb{C}}$. If there exist nonzero linear functionals
${\varphi}$ and ${\psi}$ on ${A}$ satisfying ${(\iota \bigotimes \varphi)
\Delta (a) = \varphi (a) 1}$ and ${(\psi \bigotimes \iota) \Delta (a)=
\psi(a)1}$ for all ${a \in A}$ (where ${\iota}$ is the identity map
on ${A}$), then there is an antipode on ${A}$ and (${A, \Delta}$) is
a Hopf algebra. Compare this result with the notion of a locally compact
quantum group (in the von Neumann algebra setting). Given is a pair
${(M,\Delta)}$ of a von Neumann algebra M and a coproduct ${\Delta:
M \rightarrow M \bigotimes M}$ (where now the von Neumann algebraic
tensor product is considered). If there exist a left and a right Haar
weight ${\varphi}$ and ${\psi}$ on M, then ${(M,\Delta)}$ is a locally
compact quantum group. The key result in the theory of locally compact
quantum groups is the construction of the antipode from these axioms.
Then the similarity between this and the LarsonSweedler theorem for
Hopf algebras is clear. We will mainly talk about this connection. But
at the end of the talk, we will briefly indicate how the same link pops
up in the more recent work on quantum groupoids (joint work with B.J.
Kahng).

Erik van Erp
University of Hawaii at Manoa 
Some fundamental problems in the index theory of nonelliptic Fredholm
operators.
In the investigation of index formulas for nonelliptic Fredholm
operators, interesting new phenomena appear that are not apparent in
elliptic theory. In testing the boundaries of known approaches to index
problems, fundamental problems arise when we try to extend the theory
to more general Fredholm operators. I want to discuss some "negative
results" that may be of philosophical interest, partly in the hope
that a clear exposition of some of these issues might elicit new ideas
from the audience.

Qingyun Wang Washington
University in St Louis, about to join University of Toronto 
Rokhlin properties and noncommutative dimension
Given a C*dynamic system ${\alpha: G \rightarrow Aut(A)}$,
we could form the crossed product ${C*(G,A,\alpha)}$, which is again
a C*algebra, in a way similar to semiproduct of groups. ${A}$ naturally
embeds into ${C*(G,A,\alpha)}$, hence it's interesting to see what properties
of ${A}$ can be inherited by the crossed product. In this talk, I will
present several definitions of dimension for C*algebras, which are
noncommutative versions of Lebesgue's covering dimension for topological
spaces. Then I'll show that when the action ${\alpha}$ is nice, namely
having the Rokhlin properties, the property on ${A}$ of having dimension
${<k}$ will be inherited by the crossed products.

Stanisław Woronowicz
University of Warsaw

Wave operators and quantum groups in the C*setting
Wave operators appeared first in the quantum scattering theory.
From the mathematical point of view they belong to the perturbation
theory of selfadjoint operators. We shall show, that after a suitable
modification they are useful when we construct examples of locally compact
quantum groups. The set of presented examples will include the (unpublished
as of yet) quantum ‘ax + b’group with Schmudgen commutation
relations.

Guoliang Yu
Texas A&M University

Ktheory of C* algebras associated to Hilbert manifolds and applications
I will introduce a ${C^*}$algebra associated to Hilbert
manifolds and discuss its applications to the Novikov conjecture for
a certain diffeomorphism group. This is joint work with Jianchao Wu
and Erik Guentner.
