Upcoming Seminars:
every Tuesday and Thursday at 2 pm Room 210 
May 8, 2014
2.10pm FI210

Claire Shelly
Skein Theory for D^(3n) Planar Algebras
In this talk we will review a construction of the D^(3n) subfactors
and give a presentation of their (A_2) subfactor planar algebra in
terms of generators and relations.

Past Seminars 
May 1, 2014
2.10pm FI210

Hannes Thiel
The generator problem for C*algebras
The generator problem asks to determine for a given C*algebra the
minimal number of generators, i.e., elements that are not contained
in a proper C*subalgebra. It is conjectured that every separable,
simple C*algebra is generated by a single element. The generator
problem was originally asked for von Neumann algebras, and Kadison
included it as Nr. 14 of his famous list of 20 "Problems on von
Neumann algebras". The general problem is still open, most notably
for the free group factors.
With Wilhelm Winter, we proved that every a unital, separable C*algebra
is generated by a single element if it tensorially absorbs the JianSu
algebra. This generalized most previous results about the generator
problem for C*algebra.
In a different approach to the generator problem, we define a notion
of `generator rank', in analogy to the real rank. Instead of asking
if a certain C*algebra A is generated by k elements, the generator
rank records whether the generating ktuples of A are dense. It turns
out that this invariant has good permanence properties, for instance
it passes to inductive limits. It follows that every AFalgebra is
singly generated, and even more the set of generators is generic (a
dense G_deltaset).

April 22, 2014
2.10pm FI210

Dave Penneys
Frobenius algebras in rigid C*tensor categories
Frobenius algebras in unitary fusion categories give
subfactors by work of many people, including LongoRehren and Mueger,
which show this result for subfactors of type III factors. We will
give a straightforward proof for type II_1 factors.

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.

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.
