SCIENTIFIC PROGRAMS AND ACTIVITIES

May 29, 2017

THE FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES

February 5-7, 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


Registration on site
Fee: \$50 for faculty,
\$30 for postdocs, \$20 for students.
Fee waived for invited speakers
Schedule Abstracts
Participant List Getting to UOttawa
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 Tannaka-Krein 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 non-trivial 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
9:30-10:00: Registration & coffee
10:00-10:50:

Jhong-Zin Ruan, University of Illinois at Urbana-Champaign
Exotic Quantum Group C*-algebras.

11:00-11:50:

Douglas Farenick, University of Regina
Operator systems from discrete groups.

12:00-12:50:

Matthew Kennedy, Carleton University
C*-simplicity and the unique trace property for discrete groups.

12:50-14:10:

Lunch break

14:10-15:00: David Handelman, University of Ottawa
Good and not-so-good traces on (AF) C*-algebras
15:00-15:30:

Coffee break

15:30-16:20:

Charles Starling, University of Ottawa
Boundary Quotients of Semigroup C*-algebras -- Slides

16:30-17:20:

Nico Spronk, University of Waterloo
Weak amenability of Fourier algebras -- Slides

Friday February 6
9:10-10:00:

Roland Vergnioux, Université de Caen Basse-Normandie
Stabilizer subgroups of universal compact quantum groups and the Connes embedding property

10:00-10:20:

Coffee break

10:20-11:10:

James A. Mingo, Queen's University
Freeness and the Transpose -- Slides

11:20-12:10:

Richard Blute, University of Ottawa
Hopf Algebras and The Logic of Tensor Categories -- Slides

12:10-14:10: Lunch break
14:10-15:00: Sutanu Roy, University of Ottawa & Carleton University
Quasitriangular quantum group twisted tensor product of C*-algebras
15:00-15:30: Coffee break
15:30-16:30: CRM distinguished lecture:
Stanislaw Lech Woronowicz, IMPAN-Warsaw
Categories of C*-algebras subject to an action of a quantum group
16:30-18:00: Discussion
Saturday February 7
9:10-10:00: Matthias Neufang, Carleton University
Amenability and injectivity of locally compact quantum groups
10:00-10:20: Coffee break
10:20-11:10 Jason Crann, Carleton University
A unified framework for complementarity in quantum information -- Slides
11:20-12:10 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
Beauvais-Feisthauer, 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
Gaudreau-Lamarre, Pierre University of Ottawa
Georgescu, Magdalena University of Toronto
Giordano, Thierry University of Ottawa
González-Guillén, 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, Zhong-Jin University of Illinois at Urbana-Champaign
Saber, Hicham University of Ottawa
Scott, Philip University of Ottawa
Spronk, Nico University of Waterloo
St-Jules, Michael University of Ottawa
Starling, Charles University of Ottawa
Vergnioux, Roland Université de Caen Basse-Normandie
Viola, Grazia Lakehead University
Woronowicz, Stanisław Lech    IMPAN-Warsaw