Operator Algebras and Quantum Groups

Operator Algebras and Quantum Groups
conference in honour of S. L. Woronowicz's seventieth birthday

12-23 September, 2011, Warsaw

S.L. Woronowicz

The conference was organized by the Stefan Banach International Mathematical Center, Department of Mathematical Methods in Physics, Faculty of Physics and University of Warsaw. The main topics of the conference were:

  • Operator algebras
  • Topological quantum groups
  • Hopf algebras
  • Noncommutative geometry

The conference was a successor of the 1995 (6.11-01.12) minisemester "Quantum Groups and Quantum Spaces"and the 2001 (17-29.09) conference "Noncommutative Geometry and Quantum Groups" hosted by the Banach Center.

The theory of operator algebras is the oldest topic in the list above. It spans areas as distant as K-theory and index theory on one hand through representation theory to ergodic theory and applications to models of theoretical physics on the other. It shapes the language and methods of the remaining three fields of reserach. It is worth noting that most mathematicians working on topics contained in the scope of the conference come from operator algebra background.

The topological point of view on quantum groups is immensely influenced by the theory of operator algebras. The purely algebraic topic of Hopf algebras connects to the analytic (or topological) theory of quantum groups through the theory of compact quantum groups and so called algebraic quantum groups. The striking feature of this theory is that several approaches like the purely algebraic, C*-algebraic or one through the theory of von Neumann algebras yield equivalent theories. Moreover, the interplay between different aspects of the theory of quantum groups has profound implications.

The leitmotif of the conference was the work of professor S.L. Woronowicz whose contributions to the foundations of quantum group theory and operator algebras cannot be overestimated and whose seventieth birthday was celebrated during the event.

Organizing Committee

  • Wiesław Pusz - coordinator
  • Piotr M. Sołtan - secretary
  • Piotr M. Hajac
  • Paweł Kasprzak
  • Piotr Stachura

Scientific Committee

  • Prof. Marc A. Rieffel (UC Berkeley)
  • Prof. K. Schmüdgen (Universität Leipzig)
  • Prof. S. Vaes (KU Leuven)
  • Prof. A. Van Daele (KU Leuven)


Monday, September 19
Session chairman: Erling Størmer
9:00-9:15 Opening
9:15-10:00Magnus Landstadt (Trondheim): Totally disconnected quantum groups.
10:15-11:00 Sergey Neshveyev (Oslo): Drinfeld twists and invariant cohomology of quantum groups
11:30-12:15 Paul F. Baum (Penn State): K-homology and [Q,R]=0
Session chairman: Michel Enock
14:45-15:30 Sergio Doplicher (Rome): Superselection structure in local quantum theories with (neutral) massless particles
15:40-16:25 Mariusz Wodzicki (Berkeley): Credit card renormalization
16:55-17:25 Elmar Wagner (Mexico): Noncommutative spin geometry of the standard Podleś sphere
17:30-18:00 Alexander Helemskii (Moscow): Metric projectivity and freedom for normed and operator modules
Tuesday, September 20:
Session chairman: Laszló Zsidó
9:00-9:45 Stefan Vaes (Leuven): Rigidity and classification for von Neumann algebras
10:00-10:45 Masamichi Takesaki (Berkeley): Invariants and model construction of group actions and outer actions on a factor
11:15-12:00 Konrad Schmüdgen (Leipzig): Unbounded operators and C* -Algebras
12:15-13:00 Shuzhou Wang (Georgia): Simple compact quantum groups.
Session chairman: Marek Bożejko
14:30-15:15 Erling StØrmer (Oslo): Positive linear maps of operator algebras
15:20-16:05 Władysław A. Majewski (Gdańsk): On the structure of the set of positive maps
16:35-17:05 Bhowmick Jyotishman (Trondheim): Quantum group of unitaries and quantum automorphisms
17:10-17:40 Sutanu Roy (Göttingen): Homomorphisms of quantum groups.
Wednesday, September 21
Session chairman: Alfons Van Daele
9:00-9:45 Joachim Cuntz (Münster): C*-algebras and number fields
10:00-10:45 Michel Hilsum (Paris): Invariance of Godbillon-Vey map by absolutely continuous conjugacies.
Session chairman: Adam Skalski
11:15-11:45 Marat Aukhadiev (Kazan): Infinite compact quantum semigroup
11:50-12:20 Joachim Zacharias (Nottingham): Higher Rokhlin properties of actions on C*-algebras
12:25-12:55 Vasyl Ostrovskyi (Kiev): On representations of real q-plane.
Session chairman: Konrad Schmüdgen
14:30-15:15 Marek Bożejko (Wroclaw): Groups and probability
15:20-16:05 Romuald Lenczewski (Wrocław): Matricial freeness and matricial R-transform
16:35-17:20 Laszló Zsidó (Rome): On Woronowicz's approach to the Tomita-Takesaki Theory
17:30-18:15 Ryszard Nest (KØbenhavn): Towards quantum Hamiltonian action
Thursday, September 22
Session chairman: Krzysztof Gawędzki
9:00-9:45 David Kyed (Göttingen): Amenability for subalgebras in finite von Neumann algebras
10:00-10:45 Jerzy Lukierski (Wrocław): Noncommutative quantum free firlds and deformed Poincare symmetries
11:15-12:00 Andrzej Sitarz (Kraków):ĸ-Minkowski star product and its symmetries.
12:15-13:00 Michel Enock (Paris): Measured quantum groupoids. Definition, actions, Morita equivalence, deformation by 2-cocycles.
Session chairman: Yasuyuki Kawahigashi
14:30-15:15 Alfons Van Daele (Leuven): Weak multiplier Hopf algebras
15:20-16:05 Jean-Michel Vallin (Orléans): On examples of finite quantum groupoids and subfactors
16:35-17:05 Thomas Timmermann (Münster): Transformation quantum groupoids in the setting of operator algebras
17:10-17:40 Pekka Salmi (Waterloo): Idempotent states and contractive idempotents on quantum groups
Friday, September 23
Session chairman: Andrzej Sitarz
9:00-9:45 Teodor Banica (Cergy-Pontoise): Quantum permutation groups: an overview
10:00-10:45 Tomasz Brzeziński (Swansea): Bundles over qunatum projective spaces
Session chairman: Sergey Neshveyev
11:15-12:00 Yasuyuki Kawahigashi (Tokyo): Superconformal field theory and noncommutative geometry
12:05-12:35 Erik Koelink (Nijmegen): The quantum group analogue of SU (1, 1) and special functions
12:40-13:10 Ulrich Krähmer (Glasgow): Noncommutative differential calculi from Hopf algebroids



  • L. Arambašić (Zagreb)
  • M. Aukhadiev (Kazan)
  • G. A. Bagheri Bardi (Persian Gulf University)
  • D. Bakić (Zagreb)
  • T. Banica (Cergy-Pontoise)
  • P. F. Baum (Penn State)
  • J. Bhowmick (Oslo)
  • M. Bożejko (Wrocław)
  • T. Brzeziński (Swansea)
  • D. Chruściński (Toruń)
  • J. Cuntz (Münster)
  • K. De Commer (Roma)
  • J. Dereziński (Warsaw)
  • S. Doplicher (Roma)
  • M. Eckstein (Kraków)
  • M. Enock (Paris)
  • K. Gawędzki (Paris)
  • K. Grabowska (Warsaw)
  • J. Grabowski (IMPAN)
  • P. M. Hajac (IMPAN)
  • A. Helemskii (Moscow)
  • N. Higson (Penn State)
  • M. Hilsum (Paris)
  • J. Jezierski (Warsaw)
  • B. -J. Kahng (Buffalo)
  • P. Kasprzak (Warsaw)
  • Y. Kawahigashi (RIMS Kyoto)
  • R. Kerner (Paris)
  • J. Kijowski (Warsaw)
  • M. Kalinowski (Warsaw)
  • E. Kölink (Nijmegen)
  • U. Krähmer (Glasgow)
  • P. Kruszyński (Son en Breugel)
  • J. Kuzentsova (Luxembourg)
  • D. Kyed (Göttingen)
  • M. B. Landstad (Trondheim)
  • R. Lenczewski (Wrocław)
  • J. Liszka-Dalecki (Warsaw)
  • J. Lukierski (Wrocław)
  • W. Majewski (Gdańsk)
  • P. Majewski (Warsaw University)
  • A. A. Mamoon (Al-Hussein Bin Talal University)
  • T. Maszczyk (Warsaw)
  • Y. Nakagami (Japan's Women's University)
  • M. Napiórkowski (Warsaw)
  • S. Neshveyev (Oslo)
  • R. Nest (København)
  • P. Olczykowski (Kraków)
  • V. Ostrovskyi (Kiev)
  • A. Paszkiewicz (University of Łódź)
  • P. Podleś (Warsaw)
  • D. Proskurin (Kiev)
  • W. Pusz (Warsaw)
  • L. Pysiak (Warsaw University of Technology)
  • S. Roy (Göttingen)
  • J. Rudnik (IMPAN)
  • G. Rudolph (Leipzig)
  • P. Salmi (Waterloo)
  • Y. Savchuk (Leipzig)
  • K. Schmüdgen (Leipzig)
  • A. Sitarz (Kraków)
  • A. Skalski (IMPAN)
  • P. M. Sołtan (Warsaw)
  • A. Sliżewska (Białystok)
  • P. Stachura (Warsaw University)
  • E. Størmer (Oslo)
  • A. Strasburger (Warsaw)
  • M. Takesaki (UCLA)
  • T. Timmermann (Münster)
  • P. Urbański (Warsaw)
  • S. Vaes (Leuven)
  • L. Vainerman (Caen)
  • J. M. Vallin (Orléans)
  • A. Van Daele (Leuven)
  • C. Voigt (Münster)
  • E. Wagner (Mexico)
  • S. Wang (Georgia)
  • M. Wodzicki (Berkeley)
  • W. Wojtyński (Warsaw)
  • S. L. Woronowicz (Warsaw)
  • J. Zacharias (Nottingham)
  • A. Zając (Kraków)
  • L. Zsidó (Roma)

Conference poster