Upcoming Seminars:
every Tuesday and Thursday at 2 pm Room 210 
April 17, 2014
2:10 pm FI210,

Eusebio Gardella
Classification of circle actions on Kirchberg algebras.
In this talk we will outline the classification of circle
actions with the Rokhlin property on Kirchberg algebras in
terms of their fixed point algebra together with the KKclass
of its predual automorphism. We will also consider a continuous
analog of the Rokhlin property, asking for a continuous path
of unitaries instead of a sequence, and show that circle actions
with the continuous Rokhlin property on Kirchberg algebras
are classified by their fixed point algebra, and in the presence
of the UCT, by their equivariant K theory. We moreover characterize
the Ktheoretical invariants that arise from circle actions
with the continuous Rokhlin property on Kirchberg algebras.


Ongoing Seminars 
Past Seminars 
April 15, 2014
3.30pm in FI210,

Martino Lupini
Conjugacy and cocycle conjugacy of automorphisms of the Cuntz
algebra are not Borel
I will present the result, obtained in joint work with
Eusebio Gardella, that the relations of conjugacy and cocycle
conjugacy of automorphisms of the Cuntz algebra O_2 are
not Borel. I will focus on the motivations and implications
of such result, and I will provide the main ideas of the
proof. No previous knowledge of descriptive set theory will
be assumed.

April 4
Time: 3:30 p.m.
Location: BA1160

Narutaka Ozawa
Noncommutative real algebraic geometry of Kazhdan's property
(T)
I will start with a gentle introduction to the emerging
(?) subject of "noncommutative real algebraic geometry,"
a subject which deals with equations and inequalities in
noncommutative algebra over the reals, with the help of
analytic tools such as representation theory and operator
algebras. I will mention some results toward Connes's
Embedding Conjecture, and then present a surprisingly simple
proof that a finitely generated group has Kazhdan's property
(T) if and only if a certain equation in the group algebra
is solvable. This suggests the possibility of proving property
(T) for a given group by computers. arXiv:1312.5431

April 1 
Rui Okayasu
Haagerup approximation property for arbitrary von Neumann
algebras
We attempt presenting a notion of the Haagerup approximation
property for an arbitrary von Neumann algebra by using its
standard form. We also prove the expected heredity results
for this property. This is based on a joint work with Reiji
Tomatsu.

March 31
4.10pm in BA6183 
James Lutley
Finite dimensional approximations of product systems
Product systems have been the subject of recent study as
a generalization of the Pimsner construction which contains
the algebras of higher rank graphs as well as crossed products
by certain partially ordered groups and a large class of
reduced semigroup C* algebras. We will discuss a particularly
wellbehaved class of such algebras with built in representations
of a remarkable form. We then look at when these algebras
are QD, when they are AF and when they are nuclear.

March 25
3.30pm in FI210

Sherry Gong
Finite Part of Operator $K$Theory and Traces on Reduced
$C^*$ Algebras for Groups with Rapid Decay
This talk is about the part of the operator $K$ theory
of groups arising from torsion elements in the group. We
will see how idempotents arise from torsion elements in
a group, and discuss the part of $K$ theory they generate,
and in particular, how to detect such idempotents using
traces. We conclude with a condition for when such elements
can be detected in the case of groups of rapid decay. We
further analyse traces on the reduced $C^*$ algebras of
hyperbolic groups and in doing so completely classify such
traces.

March 20
3.30pm in FI210 
Guihua Gong
Classification of AH algebras with ideal property, Elliott
invariant and Stevens Invariant
In this talk, I will present the classification of AH
algebra with ideal property with no dimension growth.
The talk is based on three joint papers, two papers for
reduction theorem which are joint with JiangLiPasnicu,
and one for isomorphism theorem which is joint with JiangLi.
Also I would like to discuss Kun Wang's work about the
equivalence between Elliott invariant and Stevens invariant,
which can be used to give two different descriptions of
the invariants for the classification of our class.

March 18

Yanli Song
Verlinde ring, crossed product and twisted Khomology
Let G be a compact, simply connected Lie group and \A
is a DixmierDouady bundle over G. All the sections of \A
vanishing at infinity forms a GC*algebra A. The Khomology
of A is defined to be the twisted Khomology. FreedHopkinsTeleman
shows that twisted K homology is isomorphic to the Verlinde
ring R_{k}(G). In this talk, I will try to generalize their
result to the crossed product case and prove that the Khomology
of the crossed product of A is isomorphic sort of “formal
Verlinde module”.

March 13
2.10pm in FI 210 
Joav Orovitz
Nuclear dimension and Zstability.
I will speak about the recent result of Sato, White, and
Winter. Namely, Zstability implies finite nuclear dimension
for the class of simple, separable, unital, nuclear C*algebras
with a unique tracial state.

March 11
2.10pm in FI 210, 
Ilijas Farah
Model theory and C*algebras
Is there a way of constructing separable, nuclear C*algebras
that radically differs from the classical constructions?
I will present some preliminary results on this problem,
subsuming some recent projects and work in progress with
a number of logicians and operator algebraists.

March 6 
Zhuang Niu
The classification of rationally tracially approximately pointline
algebras
I’m going to briefly describe a classification result
on the rationally tracially approximately pointline algebras.
Then I’ll discuss the range of the invariant for this
class of C*algebras. This is based on a joint work with
Guihua Gong and Huaxin Lin.

Feb. 27 
Shuhei Masumoto, University of Tokyo
A Definition of CCC for C*Algebras
In this talk, I will define the countable chain condition
(CCC) for C*algebras. In case of von Neumann algebras this
is equivalent to $\sigma$finiteness of the center. Then
I will investigate the relation between this condition and
minimal tensor products by using a set theoretic principle,
Martin's Axiom.

Feb. 25 
Qingyun Wang
Tracial Rokhlin property for actions of discrete amenable
groups on C*algebras
In this talk, I'll define a version of the (weak) tracial
Rokhlin property for actions of discrete amenable groups
acting on a unital simple separable C*algebra. It is a
generalization of the tracial Rokhlin property defined for
actions of finite groups and the integer group. I'll then
show that several known structural results about the crossed
product could be generalized to our case. Then I will give
some examples of amenable group actions on the JiangSu
algebra \mathcal{Z} with the tracial Rokhlin property, and
use it to show that actions with tracial Rokhlin property
are generic for \mathcal{Z}stable C*algebras.


Please note the Minicourses on Group Structure,
Group Actions and Ergodic Theory will be on, so the next seminar
will be on February 20, 2014 
Feb. 6 
Sutanu Roy
Quantum grouptwisted tensor product of C*algebras
We put two C*algebras together in a noncommutative tensor
product using quantum group actions on them and a bicharacter
relating the two quantum groups that act. We describe this
twisted tensor product in two equivalent ways, based on
certain pairs of quantum group representations and based
on covariant Hilbert space representations, respectively.
This is a joint work with Ralf Meyer and Stanisław
Lech Woronowcz.
Please note the Minicourses on Group Structure, Group
Actions and Ergodic Theory will be on, so the next seminar
will be on February 20, 2014

Feb. 3 
N. Christopher Phillips (University of Oregon)
A survey of $L^p$ operator algebras
In this talk, I will give a general survey of what is known
about several classes of examples of operator algebras on
$L^p$ spaces. I will also give some open questions (but
there are many more than there is time for in the talk).
I will describe results on:
Spatial $L^p$ analogs of UHF algebras (simplicity and Ktheoretic
classification).
A more general class of $L^p$ analogs of UHF algebras, in
which Banach algebra amenability is equivalent to being
isomorphic to a Spatial $L^p$ UHF algebra.
Spatial $L^p$ analogs of Cuntz algebras (simplicity, pure
infiniteness, uniqueness, and Ktheory).
Reduced $L^p$ operator transformation group algebras for
free minimal actions of discrete groups (simplicity and
traces).
Reduced $L^p$ operator group algebras for discrete groups
(simplicity for Powers groups [due to Pooya] and $L^p$ nuclearity
for amenable
groups [due to An, Lee, and Ruan]).

Jan. 30 
Eusebio Gardella
Circle actions on \mathcal{O}_2absorbing C*algebras with
the Rokhlin property
We de fine a Rokhlin property for circle actions on unital
C*algebras, and show that any circle action on a separable
\mathcal{O}_2absorbing C*algebra can be normpointwise
approximated by actions with the Rokhlin property. We also
show that if A absorbs \mathcal{O}_2 and \alpha is a circle
action on A with the Rokhlin property, then the restriction
of to any closed subgroup also has the Rokhlin property.
As an application, we classify circle actions with the Rokhlin
property on separable nuclear \mathcal{O}_2 absorbing Calgebras
up to conjugacy by an approximately inner automorphism of
the algebra. We also provide examples of how most of these
results fail if the algebra on which the circle acts is
assumed to be \mathcal{O}_\inftyabsorbing (or more speci
cally, a Kirchberg algebra) instead of \mathcal{O}_2absorbing.
If time permits, we will explain how these results could
potentially be used to classify certain not necessarily
outer automorphisms of \mathcal{O}_2.

Jan. 28 
James Lutley
The Nuclear Dimension of UCT Kirchberg Algebras
It was recently shown by Enders that the nuclear dimension
of any UCT Kirchberg algebra with torsionfree K_1 is one.
This class exactly corresponds to those which occur as graph
algebras. Here we construct a family of outstanding examples
using higher rank graphs and describe a surprisingly general
type of CPC approximation that approximates a unital inclusion
of Toeplitztype extension of said algebra into a somewhat
larger enveloping algebra. We discuss how this range defect
was corrected for in the O_n and O_inf cases and how it
might be overcome in the more general setting.

Jan. 23 
Hannes Thiel
Recasting the Cuntz category
(joint work with Ramon Antoine and Francesc Perera)
The Cuntz semigroup W(A) of a C*algebra A plays an important
role in the structure theory of C*algebras and the related
Elliott classification program. It is defined analogously
to the Murrayvon Neumann semigroup V(A) by using equivalence
classes of positive elements instead of projections.
Coward, Elliott and Ivanescu introduced the category Cu
of (completed) Cuntz semigroups. They showed that the Cuntz
semigroup of the stabilized C*algebra is an object in Cu
and that this assignment extends to a continuous functor.
We introduce a category W of (precompleted) Cuntz semigroups
such that the original definition of Cuntz semigroups defines
a continuous functor from C*algebras to W. There is a completion
functor from W to Cu such that the functor Cu is naturally
isomorphic to the completion of the functor W.
If time permits, we will apply this to construct tensor
products in W and Cu.

Jan. 21 
Max Lein
Analysis of Pseudodifferential Operators by Combining Algebraic
and Analytic Techniques
This talk will focus on a link between pseudodifferential
theory and the theory of C*algebras, socalled ${\psi}$*algebras.
Viewing pseudodifferential operators (${\psi}$DOs) as elements
of ${\psi}$*algebras, one sees that they are affiliated
to twisted crossed product C*algebras, and thus, algebraic
tools can be used to investigate properties of ${\psi}$DOs.
The talk concludes with an application, the decomposition
of the essential spectrum of a ${\psi}$DO in terms of the
spectra of a family of asymptotic ${\psi}$DOs. This makes
the intuition that »the essential spectrum is determined
by the operator's behavior at infinity« rigorous.

Nov. 28 
Alessandro Vignati
An amenable operator algebra that is not a C*algebra
Recently FarahChoiOzawa constructed a (nonseparable)
amenable operator algebra that is not isomorphic to a C*algebra,
using a particular gap discovered by Luzin. After a brief
introduction of the objects, we will explain how to generalize
their construction, in order to construct an amenable operator
algebra A such that every nonseparable amenable subalgebra
of A is not isomorphic to a C*algebra.

Nov. 26 
Dave Penneys
The operatorvalued Fock space of a planar algebra
In joint work with Hartglass, we find the operatorvalued
Fock space associated to a planar algebra. We get natural
analogs of the Toeplitz, Cuntz, and semicircular algebras,
as well as a $C^*$dynamics. These tools allow for the computation
of the Ktheory of these algebras. Certain (inductive limits
of) compressions recover CuntzKrieger, DoplicherRoberts,
and GuionnetJonesShlyakhtenko algebras.
Hongliang Yao (Nanjing University of Science and Technology)
Extensions of Stably Finite C*algebras
I will show that for any C*algebra A with an approximate
unit consisting of projections, there is a smallest ideal
I of A such that the quotient A/I is stably finite. I will
give a necessary and sufficient condition for a given ideal
to be equal to this ideal, in terms of Ktheory. I will
introduce an outline of the proof.
This talk will start at 3:30 p.m.

Nov. 21 
Dave Penneys
1supertransitive subfactors with index at most 6.2
I will begin with a brief introduction to the subfactor
classification program, which has two main focuses: restricting
the list of possible principal graphs, and constructing
examples when the graphs survive known obstructions. I will
discuss recent joint work with Liu and Morrison which classifies
1supertransitive subfactors without intermediates with
index in $(3+\sqrt{5},6.2)$. We show there are exactly 3
examples corresponding to a BMW algebra and two "twisted"
variations.

Nov. 19 
Yanli Song
An introduction to BaumConnes conjecture for the case
when G is a countable discrete group
I will outline how the HigsonKasparov C* algebra plays
a role in the proof to that conjecture.

Nov. 14 
James Lutley
C*algebras of Higher Rank Graphs
We will introduce the notion of a higher rank graph and
discuss how one generates a C*algebra from such an object.
Whereas the Cuntz algebras can be though of as being generated
by a free semigroup, graph algebras place restrictions
on multiplication, yielding a free semigroupoid construction.
Higher rank graphs generalize this by allowing paths to
admit distinct factorizations, thus introducing relations
into the semigroupoid. We will also introduce the infinite
path representation these algebras carry. The infinite path
space admits a natural locally compact Hausdorff topology
with a natural inclusion into the ktorus. We will ask if
this is might be used to compute properties of the algebra.
Emphasis will be placed on examples of wellknown algebras
which occur as higherrank graph algebras but not as conventional
graph algebras.

Nov. 12 
Qingyun Wang
mathcal{Z}stability of crossed product by actions with
certain tracial Rokhlin type property
In this talk I will present a recent paper by Ilan Hirshberg
and Joav Orovitz, where they defined a tracial notion of
\mathcal{Z}absorbing. They showed that tracially Zabsorbing
coincide with \mathcal{Z} absorbing in the simple nuclear
case. With the help of this notion, they proved that, if
$A$ is a simple nuclear \mathcal{Z}absorbing C*algebra,
then the crossed products by actions (of finite group or
integer group) satisfying certain tracial Rokhlin type property
is again \mathcal{Z}absorbing. I will then discuss some
related questions regarding nuclear dimension and strict
comparison.

Nov. 7 
James Lutley
Explicit Constructions of Kirchberg Algebras and their
Applications
After discussing the obstructions to exhibiting an arbitrary
Kirchberg algebra as a graph algebra, we will describe two
explicit generalizations which yield additional examples.
First, we will give an overview of a construction of Katsura
using an integer action with a cocycle to give all UCT
Kirchberg algebras with countable Kgroups. Katsura used
this construction to prove a remarkable theorem on the lifting
of group actions from an algebra's Kgroups to the algebra
itself. Then, for those who are interested, we can discuss
kgraphs and their algebras, and describe how to compute
the nuclear dimension of certain specific examples.

Nov. 5 
Ilijas Farah
Event InformationTitle: An amenable operator algebra
not isomorphic to a C*algebra
The algebra is a subalgebra of a finite von Neumann algebra,
2subhomogeneous, and for any e>0 we have an example
whose amenability constant is at most 1+e. The algebra is
nonseparable and I will prove that the methods used in the
proof cannot give a separable example. This is a joint work
with Y. Choi and N. Ozawa.

Oct. 29 
Martino Lupini
The algebraic eigenvalues conjecture for sofic groups
If G is a group, then the integral group ring of G is the
linear span over the integers of G inside its group von
Neumann algebra. The algebraic eigenvalues conjecture asserts
that any element of the integral group ring of G has only
algebraic integers as eigenvalues. This conjecture is still
open in general, but it has been verified by Andreas Thom
when G is sofic. I will present a short proof of Thom's
theorem in the framework of model theory for operator algebras.
No previous knowledge of model theory will be assumed.

Oct. 31 
Luis Santiago

Oct. 22 
Luis Santiago 
Oct. 24 
Yanli Song 
Oct. 17 
Dave Penneys
Free graph algebras and GJS C^*algebras
(part 2)
I will discuss ongoing joint work with Hartglass on the
C^* algebras arising from GuionnetJonesShlyakhtenko's
diagrammatic proof of Popa's reconstruction theorem for
subfactor planar algebras. I will discuss the CuntzKrieger
and ToeplitzCuntzKrieger algebras associated to a planar
algebra, and I will explain how we think they fit together
with the GJS C^*algebra of the planar algebra. We also
think there should be a nice story with the graph loop algebras
(due to many, including Evans, Izumi, Kawahigashi, Ocneanu,
and Sunder)
arising from connections on principal graphs.

Oct. 15 
Dave Penneys
Free graph algebras and GJS C^*algebras
I will discuss ongoing joint work with Hartglass on the
C^* algebras arising from GuionnetJonesShlyakhtenko's
diagrammatic proof of Popa's reconstruction theorem for
subfactor planar algebras. I will discuss the CuntzKrieger
and ToeplitzCuntzKrieger algebras associated to a planar
algebra, and I will explain how we think they fit together
with the GJS C^*algebra of the planar algebra. We also
think there should be a nice story with the graph loop algebras
(due to many, including Evans, Izumi, Kawahigashi, Ocneanu,
and Sunder) arising from connections on principal graphs.

Oct. 8 
Nicola Watson
Discrete order zero maps and nuclearity of C^*algebras
with real rank zero
Order zero maps are an integral part of the recent advances
made in the study of the structure of nuclear C*algebras.
Discrete order zero maps are a particularly nice special
case, and are, in some sense, "dense" amongst
those order zero maps with finite dimensional domain and
real rank zero codomain. Consequently, they are of particular
interest when studying both the nuclear dimension of C*algebras
with real rank zero, and more generally, when these algebras
are nuclear. As a direct consequence of the structure of
these maps we will prove a couple of results in these situations.

Tues. Oct. 3 
Claire Shelly
Planar Algebras and Type III Subfactors (Part 2)
I will begin by reviewing some basic ideas about planar
algebras and type III subfactors. Using graph algebra techniques
I will show how a type III subfactor can be used to define
a planar algebra. Finally I will discuss a simple example,
showing how planar algebras can be used to construct C^*
algebras, type III factors and subfactors.

Tues. Oct. 1 
Claire Shelly
Planar Algebras and Type III Subfactors
I will begin by reviewing some basic ideas about planar
algebras and type III subfactors. Using graph algebra techniques
I will show how a type III subfactor can be used to define
a planar algebra. Finally I will discuss a simple example,
showing how planar algebras can be used to construct C^*
algebras, type III factors and subfactors.

Thurs. Sept. 26 
James Lutley
ToeplitzCuntzKrieger algebras, CuntzToeplitz algebras
and permutations of words
We will describe a method originally due to Evans which
relates the natural Fock space representations of these
two classes of algebras, where the former is a projective
cutdown of the latter. Whereas Winter and Zacharias used
the CuntzToeplitz algebras to compute the nuclear dimension
of the Cuntz algebras, we will show progress towards computation
of that of more general CuntzKrieger algebras.

Tues. Sept. 24 
James Lutley
ToeplitzCuntzKrieger algebras, CuntzToeplitz algebras
and permutations of words
We will describe a method originally due to Evans which
relates the natural Fock space representations of these
two classes of algebras, where the former is a projective
cutdown of the latter. Whereas Winter and Zacharias used
the CuntzToeplitz algebras to compute the nuclear dimension
of the Cuntz algebras, we will show progress towards computation
of that of more general CuntzKrieger algebras.

Thurs, Sept 12 
Qingyun Wang
On the Tracial Rokhlin Property (continuing) 
Tues, Sept 10 
Yanli Song, David Barmherzig, and Qingyun Wang
Geometric KHomology and [Q, R]=0 problem
The quantization commutes with reduction problem for Hamiltonian
actions of compact Lie groups was solved by Meinrenken in
the mid1990s, and solved again afterwards by many other
people using different methods. In this talk, I will consider
a generalization of [Q, R]=0 theorem when the manifold is
noncompact. In this case, the main issue is that how to
quantize a noncompact manifold. I will adopt some ideas
from geometric Khomology introduced by Baum and Douglas
in 1980s and examine this problem from a topological perspective.
One of the applications is that it provides a geometric
model for the Kasparov KK group KK(C*(G, X), C).
David Barmherzig after tea, a continuation of last week
(report on operator algebra techniques in signal processing).

Thur Sept 5 
Luis Santiago 
Tues, Sept 3 
Qingyun Wang and David Barmherzig 
Thurs Aug15

Grazia Viola
Tracially central sequences
A central sequence in a C*algebra is a sequence that asympotically
commute in norm with every element in the algebra. The reduced
C* algebra of the free group on two generators have an
abundance of central sequences, while the group von Neumann
algebra of the group on two generators have only trivial
central sequences (where convergence is in L^2norm). To
solve this dichotomy we introduce a new notion of central
sequences, the tracially central sequences. We show that
if A is a simple, stably finite, unital, separable C*algebra,
which has strict comparison of positive elements and a unique
tracial state, and if assume also some other condition,
then the tracially central algebra of A coincide with the
central algebra of the von Neumann algebra associated to
the GelfandNaimarkSegal representation of A.

Thurs
Aug 8 
Martino Lupini
The automorphisms of a JiangSu stable C*algebra are
not classifiable up to conjugacy
After surveying various classification results for automorphisms
of C* algebras, I will explain how one can obtain negative
results about classification using tools from descriptive
set theory and, in particular, Hjorth's theory of turbulence.
As an application I will show that the automorphisms of
any JiangSu stable C*algebra are not classifiable up to
conjugacy using countable structures as invariants (joint
work with David Kerr, Chris Phillips, and Wilhelm Winter).

Tues
Aug 6 
Danny Hay
A classification result for recursive subhomogeneous algebras
Lin has shown that a C*algebra is classifiable whenever
it is tracially approximated by interval algebras (TAI)
and satisfies the Universal Coefficients Theorem. In a recent
paper of Strung & Winter, a class of recursive subhomogeneous
algebras is introduced, and classified by showing its members
are TAI. We will look at the main result and corollaries
of this paper, and discuss some of the techniques developed—the
excision of large interval algebras and finding tracially
large intervals therein.
See http://arxiv.org/abs/1307.1342

Thurs
August 1 
David Barmherzig
Mathematical Signal Processing and Operator Algebras
The classical theory of signal processing was formalized
during the last century by Nyquist, Shannon, etc. and studies
how to process, transmit, and encode information signals.
It draws heavily on techniques from Fourier theory, harmonic
analysis, complex analysis, finite field theory, and differential
equations. As well, more modern techniques have recently
been introduced such as wavelets, frame theory, compressive
sensing, and spectral graph theory methods. In recent years,
many applications of operator algebras to signal
processing have also been developed. This talk will give
an introduction and overview of these topics.

Tues
Jul 30 
James Lutley
Constructing Kirchberg Algebras from CuntzToeplitz Algebras
We will review a construction of Evans which allows us
to construct CuntzKrieger algebras from CuntzToeplitz
algebras. This construction allows us to compute the nuclear
dimension of those algebras as an extension of the method
Winter and Zacharias used to compute that of the Cuntz algebras.
Subsequently we will discuss multiple methods of
constructing algebras from infinite graphs as limits of
algebras from finite graphs such as the CuntzKrieger algebras.
Finally, we will introduce a construction of Katsura which
was recently recontextualized by Exel and Pardo that can
produce any UCT Kirchberg algebra through the implementation
of an integer action on a graph algebra.

Thurs
Jul 11 
Dave Penneys
Part 3: A new obstruction (July 11th)
In this talk, we will use Liu's relation to derive a strong
triple point obstruction. We will then recover all known
obstructions discussed in Part 1 of the talk. As an example,
we will determine the chirality of all subfactors of index
at most 4, and we will show that D_{odd} and E_7 are not
principal graphs of subfactors.

Tues
Jul 9

Dave Penneys
Part 2: Wenzl's relation (July 9th)
In this talk, we will focus on skein theory in a planar
algebra. The main goal of this talk will be to discuss two
strong quadratic relations in a subfactor planar algebra.
The first is Wenzl's relation, which is the recursive formula
for obtaining the JonesWenzl idempotents in the TemperleyLieb
planar algebra. We will talk about a variation of this relation
which holds in a general planar algebra. We will then derive
what I call Liu's relation, a clever variant of Wenzl's
relation due to Zhengwei Liu.

Mon
Jul 8,
4.10 pm
in BA6183 
Nicola Watson
Discrete order zero maps
Order zero maps are an integral part of the recent advances
made in the study of the structure of nuclear C*algebras.
Discrete order zero maps are a particularly nice special
case, and this talk will focus on just how nice they are.
Discrete order zero maps are, in some sense, "dense"
amongst those order zero maps with finite dimensional domain
and real rank zero codomain, and so they are of particular
interest when studying the nuclear dimension of C*algebras
with real rank zero. As a direct consequence of the "niceness"
of these maps we will prove a couple of results in this
situation.

Thurs
Jul 4 
Dave Penneys
Triple point obstructions, a 3 part talk
Overall abstract:
There has been recent success in the classification program
of subfactors of small index. The classification program
has two main objectives: restricting the list of possible
principal graphs, and constructing examples of subfactors
for the remaining graphs. The former task relies on principal
graph obstructions, which rule out many possibilities by
either combinatorial constraints, or by some rigidity phenomenon
which relates the local structure of the principal graph
to constants in the standard invariant of the subfactor.
A triple point obstruction is an obstruction for possible
principal graphs with an initial triple point. I will talk
about a new triple point obstruction which is strictly stronger
than all known triple point obstructions.

Part 1: Triple point obstructions (July 4th)
After a brief review of the definition of the principal
graphs of a subfactor, we will discuss the former state
of the art of triple point obstructions, including Ocneanu's
triple point obstruction, Jones' quadratic tangles obstruction,
the triplesingle obstruction of MorrisonPenneysPetersSnyder
(probably known to Haagerup), and Snyders singly valent
obstruction.

Tues
July 2 
Vitali Vougalter (University of Cape Town)
Solvability in the sense of sequences for some non Fredholm
operators
We study solvability of certain linear nonhomogeneous elliptic
problems and show that under reasonable technical conditions
the convergence in L^2(R^d) of their right sides implies
the existence and the convergence in H^2(R^d) of the solutions.
The equations involve second order differential operators
without Fredholm property and we use the methods of spectral
and scattering theory for Schroedinger type operators.
