
THE
FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES
20th
ANNIVERSARY
YEAR 
Focus
Program on Noncommutative Geometry and Quantum Groups
LECTURES
AND SEMINARS
June
37,
2013
Theme Week on Noncommutative Geometry and Dynamical Systems
Location: Stewart Library, Fields Institute
Organized by Hanfeng Li (SUNY at Buffalo),
Ian Putnam (Victoria)


Preliminary Schedule:
Monday , June
3, 2013 
9:3010:30 a.m.

David Kerr, University of Tokyo
Entropy, dynamics, and operator algebras Part 1 
10:3011:00 a.m. 
Break 
11:0012:00 noon 
Gabor Szabo, University of Muenster
The Rokhlin dimension of topological $\mathbb{Z}^m$actions
We study the topological variant of Rokhlin dimension
for topological dynamical systems $(X,\alpha,\mathbb{Z}^m)$
in the case where $X$ is assumed to have finite covering dimension.
Finite Rokhlin dimension in this sense is a property that
implies finite Rokhlin dimension of the induced action on
C*algebraic level, as was discussed in a recent paper by
Ilan Hirshberg, Wilhelm Winter and Joachim Zacharias. In particular,
it implies (in this context) that the transformation group
C*algebra has finite nuclear dimension. For a single aperiodic
homeomorphism, finite Rokhlin dimension follows easily from
a recent result by Yonathan Gutman, which in turn uses an
important property shown by Elon Lindenstrauss. We show that
their methods can be pushed to work in the realm of actions
of countably infinite groups. In the particular case of free
$\mathbb{Z}^m$actions on a fixed space $X$, application of
said methods yields a uniform bound of Rokhlin dimension that
depends only on $m$ and $\operatorname{dim}(X)$.


Lunch Break 
2:00 3:00 p.m.

Thierry Giordano, University
of Ottawa
Topological orbit equivalence and full groups Part 1 
3:003:30 p.m. 
Tea Break 
3:30 4:30 p.m. 
Leonel Robert, University of Louisiana
at Lafayette 
Tuesday, June
4, 2013 
9:3010:30 a.m.

David Kerr, University of Tokyo
Entropy, dynamics, and operator algebras Part 2 
10:3011:00 a.m. 
Break 
11:00 12:00 noon 
Nicola Watson, University of Toronto 

Lunch Break 
2:003:00 p.m.

Thierry Giordano, University
of Ottawa
Topological orbit equivalence and full groups Part 2 
3:00 3:30 p.m. 
Tea Break 
3:30 4:30 p.m. 
Mike Whittaker, University of Wollongong
C*algebras associated to selfsimilar actions and ZappaSzép
product semigroups
A selfsimilar action (G,X) consists of a group
G and finite alphabet X along with an action of the group
on the free monoid X* consisting of all finite words in the
letters of X. Mark Lawson showed that a selfsimilar action
could be realised as a ZappaSzép product semigroup
X* x G. A universal Toeplitz algebra can be constructed for
a selfsimilar action with a CuntzPimsner algebra quotient.
We show that
a generalised selfsimilar Toeplitz algebra can be constructed
for a ZappaSzép product with a boundary quotient generalising
the CuntzPimsner algebra of a selfsimilar action. We use
this to describe new presentations of C*algebras associated
to semigroups constructed by Xin Li. Some examples include
the BaumslagSolitar groups and the affine semigroup over
the natural numbers.
This is joint work with Nathan Brownlowe, Jacqui Ramagge,
and Dave Robertson.

Wednesday, June
5, 2013 
9:3010:30 a.m.

David Kerr, University of Tokyo
Entropy, dynamics, and operator algebras Part 3 
10:3011:00 a.m. 
Break 
11:0012:00 noon 
Andrew Dean, Lakehead University
Classifying actions of the reals on ${C^*}$algebras
We shall consider some classes of actions of the
reals on ${C^*}$algebras and develop invariants to
classify them up to equivariant isomorphism.


Lunch Break 
2:003:00 p.m.

Thierry Giordano, University of Ottawa
Topological orbit equivalence and full groups Part 3 
3:00 3:30 p.m. 
Tea Break 
3:304:30 p.m. 
George Elliott, University of Toronto
What is the most important from the point of view of classification?
(informal title) 
Thursday June
6, 2013 
9:3010:30 a.m.

David Kerr, University of Tokyo
Entropy, dynamics, and operator algebras Part 4 
10:3011:00 a.m. 
Break 
11:00 12:00 noon 
Bingbing Liang, SUNY at Buffalo
Mean Dimension and von NeumannL${\ddot{u}}$ck Rank
Mean dimension is a numerical invariant in topological
dynamics and related to entropy. The von NeumannLuck rank
is a L^2invariant and related to L^2 Betti number.
I will establish an equality between the von NeumannLuck
rank of a module of the integral group ring of a amenable
group and the mean dimension of the associated algebraic action.
Also I will give some applications of this equality. This
is a joint work with Hanfeng Li.


Lunch Break 
2:003:00 p.m.

Thierry Giordano, University of Ottawa
Topological orbit equivalence and full groups Part 4 
3:003:30 p.m. 
Tea Break 
3:304:30 p.m. 
Berndt Brenken, University
of Calgary
A dynamical structure for the C*algebra of a partial isometry 
Friday
June 7, 2013 
9:3010:30 a.m.

David Kerr, University of Tokyo
Entropy, dynamics, and operator algebras Part 5 
10:3011:00 a.m. 
Break 
11:00 12:00 noon 
Ian Putnam, University of Victoria
Spectral triples for subshifts
Building on ideas of Christensen and Ivan, we give
a construction for spectral triples for the crossed products
of the group of integers on a Cantor set which arise from
subshifts. We examine their basic properties.
(Joint work with A. Julien)


Lunch Break 
2:003:00 p.m. 
Gabor Szabo, University of Muenster 
3:003:30 p.m. 
Tea Break 
3:30 4:30 p.m. 
TBA 
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