OVERVIEW
This weekly seminar is devoted to applications of logic
to operator algebras. In its first semester it will feature
three types of talks: (i) introductory talks on operator algebras
aimed at logicians, (ii) introductory talks on logic aimed
at operator algebraists and (iii) discussions of recent applications
of set theory and model theory to C*-algebras and von Neumann
algebras.
In addition to these, some of the meetings will be 'working
seminars' devoted to addressing open problems or working through
the literature.
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Upcoming
Seminars
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TBA
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| Past
Seminars 2012-13 |
| Mar. 26 |
Dave Penneys
GJS C*-algebras
Guionnet-Jones-Shlyakhtenko (GJS) gave a diagrammatic proof
of a result of Popa which reconstructs a subfactor from
a subfactor planar algebra. In the process, certain canonical
graded *-algebras with traces appear. In the GJS papers,
they show that the von Neumann algebras generated by the
graded algebras are interpolated free group factors. In
ongoing joint work with Hartglass, we look at the
C * -algebras generated by the graded algebras. We are interested
in a connection between subfactors and non-commutative geometry,
and the first step in this process is to compute the K-theory
of these C * -algebras. I will talk about the current state
of our work.
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| Mar. 21 |
Makoto Yamashita
Deformation of algebras from group 2-cocycles
Algebras with graded by a discrete can be deformed using
2-cocycles on the base group. We give a K-theoretic isomorphism
of such deformations, generalizing the previously known
cases of the theta-deformations and the reduced twisted
group algebras. When we perturb the deformation parameter,
the monodromy of the Gauss-Manin connection can be identified
with the action of the group cohomology.
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| Mar. 5 |
Danny Hay
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| Feb. 28 |
Martino Lupini
C*-algebras and omytting types
I will give an introduction to model theory for operator
algebras. I will then explain how many important classes
of C*-algebras can be characterized by the model-theoretic
notion of omitting types. I will conclude presenting some
applications to the theory of UHF and AF algebras.
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| Jan. 14 |
Martino Lupini
Logic, ultraproducts and central sequence algebras
I will introduce the fundamental notions of the logic for
metric structures, among which the notiond of ultraproduct.
I will then describe and study in this framework the notion
of central sequence algebra of a unital C*-algebra, in particular
in relation to its applications in the paper "CENTRAL
SEQUENCE C*-ALGEBRAS AND TENSORIAL ABSORPTION OF THE JIANG-SU
ALGEBRA"
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| Dec 19 |
Bradd Hart, McMaster University
Model theory and operator algebra
The title is a catch all for the thesis that these two subjects
have something to do with one another. I will try to make
this point by looking at the state of our knowledge of the
continuous theory of the hyperfinite II_1 factor and its relationship
with the Connes Embedding Problem.
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| Dec 12 |
Dave Penneys
II_1 factors and subfactors 2
We will give a broad introduction to II_1 factors, starting
with some basic facts, including standard form and the coupling
constant. We will then focus on subfactors, and we will aim
to discuss some classification results.
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| Dec 5 |
Dave Penneys
A talk about II_1 factors
We will give a broad introduction to II_1 factors, starting
with some basic facts, including standard form and the coupling
constant. We will then focus on subfactors, and we will aim
to discuss some classification results.
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Nov 28
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Paul McKenney (CMU)
Automorphisms of a corona algebra
I will discuss the automorphisms of $\ell^\infty(CAR) / c_0(CAR)$,
and give an overview of the proof that, assuming Todorcevic's
Axiom and Martin's Axiom, they are all trivial.
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Nov 21
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Saeed Ghasemi (York)
Tensor products of SAW* algebras
First I will introduce SAW*-algebras as non-commutative analogous
of sub-Stonean spaces in topology and state some of the results
about sub-Stonean spaces which have been generalized by G.K.
Pedersen to SAW*-algebras. Secondly I will show that there
is no surjective *-homomorphism from SAW*-algebras into tensor
product of two infinite dimensional C*-algebras using the
corresponding result for sub-Stonean spaces, i.e. SAW*-algebras
are essentially non-factorizable.
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Nov 14
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No Seminar |
Nov 7
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Isaac Goldbring (UIC)
Pseudofinite and pseudocompact metric structures
In classical logic, an L-structure M is said to be pseudofinite
if every L-sentence which is true in all finite L-structures
is also true in M; equivalently, if an L-sentence is true in
M, then it is true in some finite L-structure. The random graph
is a pseudofinite structure and pseudofinite fields have proven
to be very interesting to model theorists. In joint work with
Vinicius Cifu Lopes, we initiate the study of pseudofinite metric
structures (in the sense of continuous logic). Due to the lack
of negations in continuous logic, the aforementioned equivalence
doesn't hold, leading to two separate notions, which we call
pseudofinite and strongly pseudofinite. By replacing finite
structures by compact structures, we obtain the related notions
of pseudocompact and strongly pseudocompact. In this talk, I
will discuss some basic properties of these notions as well
as many examples, including a connection with von Neumann algebras.
I will also discuss some interesting open questions.
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Oct. 16 &
Oct. 24
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No seminar Oct. 16 due to Fields
Medal Symposium
No seminar October 24 due to Workshop
on Forcing Axioms and their Applications, October 22-26
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Oct. 10
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Martino Lupini (York)
Connes spectrum and inner automorphisms of C*-algebras
I will introduce the Connes spectrum for automorphisms of
C*-algebras and explain how inner automorphisms can be characterized
in terms of it. |
Oct. 3
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Martino Lupini (York)
Spectrum of one-parameter groups of automorphisms and derivations
of C*-algebras
I will introduce the spectrum of a one-paramter group of
automorphisms of a C*-algebra, and present its applications
to the study of derivations. In particular, I will prove the
result of Sakai that every derivation of a simple C*-algebra
is inner, and the result of Akemann, Elliott, Pedersen and
Tomiyama that every derivation of a separable C*-algebra with
continuous trace is inner.
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Sept. 26
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Tristan Bice (Fields Institute and York)
General applications of set theory to C*-algebras
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Sept. 19
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Aaron Tikuisis (University of Muenster)
Nuclear dimension and decomposition rank |
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Sept. 5
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Luis Santiago ( University
of Oregon)
Jiang-Su algebra |
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Aug. 29
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Zhiqiang Li (University
of Toronto)
A basic introduction to KK-theory of C*-algebras
I will present some basic facts about KK-groups, and show calculation
of some concrete examples. |
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Aug. 22
1:30 p.m.
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Henning Petzka (University
of Toronto)
The Bott projection in the classification of C*-algebras
Vector bundles and Chern classes have been used to construct
C*-algebras with rather exotic behavior. In particular, the
Bott projection has played a prominent role. We will look on
some constructions of `exotic' C*-algebras, - for instance Rordam's
simple C*-algebra containing both a finite and a (non-zero)
infinite projection,- and the unifying idea behind their constructions. |
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Aug. 15
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Jorge Plazas ( Fields
Institute)
An Introduction to Noncommutative Geometry
Noncommutative geometry, largely based on the theory operator
algebras, extends the tools of geometry beyond their classical
scope leading to deep insights and applications in various areas
of mathematics. In this talk we will give a short review of
some of the key ideas of the field, introduce some of its techniques
and discuss a few examples. |
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Aug. 8
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Luis Santiago (University
of Oregon)
An Introduction to Cuntz Semigroup |
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Aug 1, 2012
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Zhiqiang Li
Introduction to KK-theory |
