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CRM > English > Activities > Curs 2016-2017 > IRP Operator Algebras: Dynamics and Interactions
IRP Operator Algebras: Dynamics and Interactions
 
March 1st to July 21st, 2017
General information
 
 
Description

The classification of simple nuclear C*-algebras has been work of many hands that has spanned over years. The AF-algebras - C* algebras that can be expressed as the norm closure of an increasing union of finite-dimensional subalgebras - constituted one of the first classes of simple C* -algebras to be classified. This was achieved by Elliott in the 1970's; his classification was essentially in terms of K-theory. But many tractable examples of simple C*-algebras lie outside this class, and the focus of classification theory quickly shifted to nuclear C*-algebras - those in which the identity map can, on any finite collection of elements, be approximately factored via two completely positive contractions, through a finite-dimensional C*-algebra. This leads to a beautiful connection back to von Neumann algebras: a separable C*-algebra is nuclear precisely when its double dual has the property of being Approximately Finite Dimensional. Inspired by von Neumann algebraic techniques developed by McDuff, and present in Kirchberg's work on purely infinite C*-algebras, Toms and Winter showed that tensorial absorption of a strongly self-absorbing C*-algebra such as the Jiang-Su algebra or the Cuntz algebra CodeCogsEqn (2).gifcan provide additional regularity properties required for a classification (using K-theoretical information) to hold.

 

These developments have resulted in a burst of activity in the area of simple nuclear C*-algebras with dramatic new advances (some very recent) in classification and structure being drivenby techniques directly analogous to those used in the classification of amenable von Neumann factors. At the same time, the rapidly-increasing scope of the theory has led to a demand for good models, akin to the realisation of AFD factors as crossed products, for each new class of C*-algebras encompassed by classification results.

 

Objectives:

This Intensive Research Program is designed simultaneously to speed up and contribute to the next game-changing developments in classification and structure theory for C*-algebras, and to prepare for the new state of play in the area once those developments arrive. According to current developments, the IRP will strive to blend different techniques coming both from C* and von Neumann algebras and find a common ground to maximise outputs. The program will bring together many of the world's leading researchers working on C*-algebras, von Neumann algebras, dynamical systems, and the interactions between these areas. There are three key objectives:

1. To advance classification programs for C*-algebras and for C*-dynamical systems.

2. To investigate further suitable models for classifiable C*-algebras arising from dynamics.

3. To encourage further interaction between C*-algebras and von Neumann algebras in light of current progress in both areas.

  

We expect the participation of young researchers, both predoctoral and postdoctoral in the activities planned during the program, particularly seminars, workshops, the intensive course and the conference.

 

Scientific organizers

 

Nathanial P. Brown​ ​The Pennsylvania State University
Francesc Perera ​ ​Universitat Autònoma de Barcelona
Aidan Sims ​ ​University of Wollongong
Stuart White​ ​University of Glasgow
Wilhelm Winter ​ ​University of Münster ​
 
Invited visiting researchers
 
JudithA. PackerUniversity of Colorado Boulder17/06/201724/06/2017
Astridan HuefUniversity of Otago18/06/201721/07/2017
RamonAntoineUniversitat Autonòma de Barcelona01/03/201721/07/2017
PereAraUniversitat Autonòma de Barcelona01/03/201721/07/2017
SaraArklintKobenhavns Universitet
JoanBosaUniversity of Glasgow01/03/201721/07/2017
Nathanial P.BrownThe Pennsylvania State University09/04/201722/04/2017
LaurentCantierUniversitat Autonòma de Barcelona01/03/201721/03/2017
JoanClaramuntUniversitat Autonòma de Barcelona01/03/201721/07/2017
JoachimCuntzUniversität Münster
MariusDadarlatPurdue University
MariusDadarlatPurdue University
SørenEilersUniversity of Copenhagen
SørenEilersUniversity of Copenhagen
George A.ElliottUniversity of Toronto
RuyExelUniversidade Federal de Santa Catarina
IlijasFarahYork University
EusebioGardellaUniversität Münster13/03/201728/04/2017
ElisabethGillaspyUniversität Münster13/03/201720/03/2017
ElisabethGillaspyUniversität Münster17/06/201725/06/2017
IlanHirshbergBen-Gurion University of the Negev
IlanHirshbergBen-Gurion University of the Negev
YasuyukiKawahigashiThe University of Tokyo
KangLiUniversität Münster20/03/201724/03/2017
XinLiQueen Mary University of London
HuaxinLinUniversity of Oregon
FernandoLledóUniversidad Carlos III
MatiasLolkUniversity of Copenhagen03/04/201724/04/2017
MartinoLupiniCalifornia Institut of Technology
MagdalenaMusatKobenhavns Universitet03/04/201724/04/2017
Chi-KeungNgNankai University
LisaOrloffUniversity of Otago15/06/201723/06/2017
EduardOrtegaNorwegian University of Science and Technology13/03/201724/03/2017
EduardOrtegaNorwegian University of Science and Technology05/06/201730/06/2017
EnriquePardoUniversidad de Cádiz13/03/201724/03/2017
EnriquePardoUniversidad de Cádiz18/04/201728/04/2017
EnriquePardoUniversidad de Cádiz19/06/201723/06/2017
FrancescPereraUniversitat Autonòma de Barcelona01/03/201621/07/2017
Christopher N.PhillipsUniversity of Oregon
Christopher N.PhillipsUniversity of Oregon
IanPutnamUniversity of Victoria
SarahReznikoffKansas State University
LeonelRobertUniversity of Louisiana at Lafayette
MikaelRordamKobenhavns Universitet03/04/201724/04/2017
EduardoScarparoUniversity of Copenhagen
AzinSharihiUniversitat Autonòma de Barcelona01/03/201721/07/2017
AidanSimsUniversity of Wollongong05/03/201725/03/2017
AidanSimsUniversity of Wollongong04/06/201724/06/2017
ChristianSkau
KarenStrungPolskiej Akademii Nauk
KarenStrungPolskiej Akademii Nauk
GaborSzabóUniversity of Aberdeen
GaborSzabóUniversity of Aberdeen
HannesThielUniversität Münster
AaronTikuisisUniversity of Aberdeen19/06/201723/06/2017
StuartWhiteUniversity of Glasgow29/05/201723/06/2017
DanaWilliamsDartmouth College11/03/201723/03/2017
WilhelmWinterUniversität Münster
JoachimZachariasUniversity of Glasgow

 

This is an automatic list updated as research visitors confirm their participation.
 
Activities

Weekly Seminar

Advanced Course on Operator Algebras: groupoids, crossed products, and Rokhlin dimension, from March 13 to 17, 2017

Workshop on C*-algebras and Dynamical Systems, from March 20 to 24, 2017

Barcelona Conference on C*-algebras: Structure, Classification and Dynamics, from June 19 to 23, 2017​

 

Acknowledgements

This program is made possible in part by the generous support from the Simons Foundation, the National Science Foundation and the Clay Mathematics Institute.

 

Further information

For inquiries about the program please contact the research program's coordinator at IRP@crm.cat.​

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