Operator Algebras and Quantum Groups
conference in honour of S. L. Woronowicz's seventieth birthday
12-23 September, 2011, Warsaw
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)
Program
| Monday, September 19 | |
|---|---|
| Session chairman: Erling Størmer | |
| 9:00-9:15 | Opening |
| 9:15-10:00 | Magnus 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 |
Abstracts
Participants
- 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)