
THE
FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES

Operator
Algebras Seminars
July 2014  June 2015
Seminars
are generally held every Tuesday and Thursday at 2:10
pm in Room 210.
Hosted by the Fields Institute


Fr
For more information about this program please contact
George Elliott


Upcoming Seminars:
every Tuesday and Thursday at 2 pm Room 210 
September 30, 2014
2:10pm

Magdalena Georgescu
Characterization of spectral flow in a type II factor
I will start with an introduction to spectral flow. In B(H) (the
set of bounded operators on a Hilbert space), the spectral flow counts
the net number of eigenvalues which change sign as one travels along
a path of selfadjoint Fredholm operators. It is possible to generalize
the concept of spectal flow to a semifinite von Neumann algebra, as
we can use a trace on the algebra to measure the amount of spectrum
which changes sign. I will give a characterization of spectral flow
in a type II factor, and a sketch of the proof.

Past Seminars 
September 29, 2014
11:00am1:00pm

Alessandro Vignati
On what I learnt in Glasgow about the UCT (Part 2)
After the reviewing on the basic definitions related to TAF algebras,
I will give a proof of the fact that, in the TAF simple case, homotopic
*homomorphisms are necessarily approximately unitarily equivalent.
If there is a time I will sketch an idea of how to prove that KKequivalent
*homs are approximately unitarily equivalent, passing through the
mod n KKtheory.

September 25, 2014
2:10pm 
Juno Jung 
September 23, 2014
2:10pm 
Jeffery Im
Finite nuclear dimension from Zstability in the unique trace case
We report on a proof of the main result in a paper of Sato, White,
and Winter which establishes finite nuclear dimension from Zstability
for the usual TomsWinter C*algebras with a unique tracial state.
A key idea here, which also appeared in an earlier paper of Matui
and Sato, is the twocolored approximately inner flip. The end result
is the estimate dr(A) < 4 obtained by using UHFstable approximations
twice, with each approximately inner flip contributing two colors.

September 22, 2014
11:00am1:00pm

Alessandro Vignati
On what I learnt in Glasgow about the UCT (Part 1)
I will present an introduction on the UCT and KKtheory and a collection
of results related to the UCT in the TAF case. This seminar will follow
the lectures of Marius Dadarlat and Christian Voigt in a recent Masterclass
in Glasgow.

August 21, 2014
2:10pm

Jeffrey Im,
Nuclear dimension and Zstability
We will sketch the original construction of the JiangSu algebra
and discuss some of its properties. Apart from serving as the first
(and only) example of its kind, understanding its role in K theoretic
classification of simple separable nuclear of C*algebras has been
of great interest in recent years. A number of results indicate that
the largest class of C*algebras for which Elliott's classification
conjecture can hold is for those which are also Z stable. Various
disparate regularity properties, each of which is helpful for classification,
arise as a consequence of being Zstable. A wellknown conjecture
characterizing manifestations of Zstability in a certain class of
C*algebras is the TomsWinter conjecture. We discuss one of the properties,
finite nuclear dimension, and progress on the conjecture.

August 21, 2014
3:15 pm 
Juno Jung,
The necessity of quasidiagonality and unique tracial states
On Matui and Sato's paper, titled "Decomposition rank of UHF
absorbing C*algebras'", proves that if A is a unital separable
simple C*algebra with a unique tracial state, then if A is nuclear,
quasidiagonal and has strict comparison or projections, then the decomposition
rank of A is at most 3. As a corollary, a partial affirmation of the
Toms and Winters conjecture can be proven. In this talk, we focus
on how quasidiagonality and having a unique tracial state are necessary
conditions for this theorem.

August 19, 2014

James Lutley, University of Toronto
AF algebras of higher rank graphs
We will introduce sufficient and necessary conditions to ensure
that the algebras associated with a higher rank graph are AF. These
algebras are the Toeplitz extension, which has a representation on finite
paths, and the main algebra, represented on infinite paths, which correspond
to ultrafilters of the finite path space. We will discuss what obstructions
exist, and whether or not the quotient can be AF when the Toeplitz extension
is not.

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