
THE
FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES
February
57, 2015
Workshop on
Recent Developments in Quantum Groups, Operator
Algebras and Applications
at the University of Ottawa


Organizing
Committee
Benoit Collins  University of Ottawa
Thierry Giordano – University of Ottawa
Sutanu Roy  University of Ottawa and Carleton
University
Scientific
Advisory Committee
George A. Elliott  University of Toronto
Kenneth R. Davidson  University of Waterloo
Stanislaw L. Woronowicz  University of Warsaw





The registration and the
talks will take place in the Department of Mathematics and Statistics, uOttawa.
Map of Campus.
OVERVIEW
From the late 1980's, S. L. Woronowicz defined and studied C*algebra approach
to quantum groups. In particular in the compact case, he proved a generalization
of the TannakaKrein duality theory using C*tensor categories. This approach
provides close connections between quantum groups and other important research
topics as quantum field theory, knots, and von Neumann subfactors.
It is only in 2000, that J. Kustermans and S. Vaes gave a satisfactory definition
of a general locally compact quantum group. Presence of Haar weights allows
to peform harmonic analysis on locally compact quantum groups, including generalization
of several results for locally compact groups.
The first nontrivial examples of quantum groups were given by Woronowicz
himself (who participates to the meeting). One next big family of quantum
groups was given by Wang around 1995  the so called free quantum groups.
Their representation theory and their first operator algebraic theory were
unveiled by Banica. Later on, together with Bichon, Collins and others, important
relations with free probability were discovered.
However, the operator algebraic structures remained difficult to understand
until Vergnioux  who participates to the meeting (and then Vergnioux and
Vaes) introduced the notion of rapid decay in the context of quantum groups.
Their results have subsequently inspired dozens of results about the structure
of the von Neumann algebras of quantum groups (solidity, factoriality, primeness,
etc)
On the other hand, the notion of amenability is a very important one in the
context of quantum groups, and many progress have been made in this direction
in the context of locally compact quantum groups (Crann, Kalantar).
Finally, lately there has been new promising relations between quantum groups
and quantum information theory (initiated in particular by Junge, Ruan, Neufang
and Crann), and also between quantum groups and logic (that is represented
by many experts at uOttawa).
Many important actors of quantum groups theory will attend and their presence
will be a great benefit to the mathematical community of Ontario. We expect
that graduate students from Ontario and nearby universities will also benefit
from this aggregation of experts.
Finally, experts from different backgrounds expect to learn from each others'
expertises in order to develop new directions of research on the occasion
of this workshop.
Schedule
Thursday February
5 
9:3010:00: 
Registration & coffee 
10:0010:50: 
JhongZin Ruan, University of Illinois at UrbanaChampaign
Exotic Quantum Group C*algebras.

11:0011:50: 
Douglas Farenick, University of Regina
Operator systems from discrete
groups.

12:0012:50: 
Matthew Kennedy, Carleton University
C*simplicity and the unique trace
property for discrete groups.

12:5014:10: 
Lunch break

14:1015:00: 
David Handelman, University of Ottawa
Good and notsogood traces on (AF)
C*algebras

15:0015:30: 
Coffee break

15:3016:20: 
Charles Starling, University of Ottawa
Boundary Quotients of Semigroup
C*algebras  Slides

16:3017:20: 
Nico Spronk, University of Waterloo
Weak amenability of Fourier algebras
 Slides

Friday February
6 
9:1010:00: 
Roland Vergnioux, Université de Caen BasseNormandie
Stabilizer subgroups of universal
compact quantum groups and the Connes embedding property

10:0010:20: 
Coffee break

10:2011:10: 
James A. Mingo, Queen's University
Freeness and the Transpose
 Slides

11:2012:10: 
Richard Blute, University of Ottawa
Hopf Algebras and The Logic of Tensor
Categories  Slides

12:1014:10: 
Lunch break 
14:1015:00: 
Sutanu Roy, University of Ottawa & Carleton University
Quasitriangular quantum group twisted
tensor product of C*algebras

15:0015:30: 
Coffee break

15:3016:30: 
CRM distinguished lecture:
Stanislaw Lech Woronowicz, IMPANWarsaw
Categories of C*algebras subject
to an action of a quantum group

16:3018:00: 
Discussion

Saturday February 7 
9:1010:00: 
Matthias Neufang, Carleton University
Amenability and injectivity of locally
compact quantum groups 
10:0010:20: 
Coffee break 
10:2011:10 
Jason Crann, Carleton University
A unified framework for complementarity
in quantum information  Slides

11:2012:10 
Grazia Viola, Lakehead University
Classification of spatial $L^p$ AF algebra
 Slides

Participant List
Full Name 
University/Affiliation 
Al Nuwairan, Muneerah 
University of Ottawa 
Bagnol, Marc 
University of Ottawa 
BeauvaisFeisthauer, Joey 
University of Ottawa 
Blute, Richard 
University of Ottawa 
Buteau, Samuel 
University of Ottawa 
Cioppa, Timothy 
University of Ottawa 
Collins, Benoît 
University of Ottawa 
Cordeiro, Luiz Gustavo 
University of Ottawa 
Crann, Jason 
Carleton University 
Farenick, Douglas 
University of Regina 
Forrest, Brian 
University of Waterloo 
Furber, Robert 
Radboud University, Nijmegen 
GaudreauLamarre, Pierre 
University of Ottawa 
Georgescu, Magdalena 
University of Toronto 
Giordano, Thierry 
University of Ottawa 
GonzálezGuillén, Carlos 
University of Ottawa 
Hamzo, Chadi 
University of Ottawa 
Handelman, David 
University of Ottawa 
Hosseini, Maryam 
University of Ottawa 
Kennedy, Matthew 
Carleton University 
Khan, Sakif Hossain 
University of Ottawa 
Mehta, Arthur 
Carleton University 
McDonald, Alexander 
University of Ottawa 
Mingo, James A. 
Queen's University 
Neufang, Matthias 
Carleton University 
Rakotoarisoa, Tantely 
University of Ottawa 
Roumen, Frank 
Radboud University, Nijmegen 
Roy, Sutanu 
University of Ottawa & Carleton University 
Ruan, ZhongJin 
University of Illinois at UrbanaChampaign 
Saber, Hicham 
University of Ottawa 
Scott, Philip 
University of Ottawa 
Spronk, Nico 
University of Waterloo 
StJules, Michael 
University of Ottawa 
Starling, Charles 
University of Ottawa 
Vergnioux, Roland 
Université de Caen BasseNormandie 
Viola, Grazia 
Lakehead University 
Woronowicz, Stanisław Lech 
IMPANWarsaw 

