Updated 7 December 2001
Upcoming
seminar activity
During the
period 1 October - 31 December 2001, when the research group
"Non-Commutative Phenomena in Mathematics and Theoretical Physics" at
the Centre for Advanced Study will concentrate on operator algebras, the
C*-seminar will be held at the Centre, and there will also be some extra
seminars in addition to the usual time Wednesday. People who want to partake in
lunch at the Centre at 12:00 before the seminar should give notice at least 3
hours in advance.
For past
seminar and workshop activity, see some distance below.
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The program for
the nearest period is (the closer the dates, the more definite the program):
Wednesday 12/12
13:15 – 15:00
Nadia S.
Larsen, Copenhagen
"Representations
of Hecke algebras, dilations of semigroup crossed products and
applications"
Monday 17/12
13:15 – 15:OO
Michael
Müger, Amsterdam / Lars Tuset, Oslo
"Reconstruction
theorems for tensor C*-categories"
Wednesday 19/12
13:15 – 15:00
Steve
Kaliszewski, Arizona
"Naturality
and Induced Representations for C*-Dynamical Systems"
Abstract. We
show that induction of covariant representations for C*-dynamical systems is
natural in the sense that it gives a natural transformation between certain
crossed-product functors. This involves setting up suitable categories of
C*-algebras and dynamical systems, and extending the usual constructions of crossed
products to define the appropriate functors. From this point of view, Green's
Imprimitivity Theorem identifies the functors for which induction is a natural
equivalence. Various special cases of these results have previously been
obtained on an ad hoc basis.
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A
homepage for the
research group with links from
http://www.shs.uio.no/Groups/index.html
will
(hopefully) be established before the end of the world. In the meantime, see
http://www.math.uio.no/~bratteli/SHS/info.html .
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------------
Address
of the Centre for Advanced Study:
Drammensveien 78, 0271 Oslo (next to the Russian embassy)
The entrance is
an inconspicious door behind the left side of the Academy building,
see http://www.shs.uio.no/ .
Ring the door bell and go up the stairs to the third floor lobby, where the
seminar room is.
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------------
Note
to the speakers: There
are two relatively small blackboards (which may be turned into whiteboards) in
the seminar room. It is convenient to use transparencies (there are two
overhead projectors).
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Complete list of operator algebraists who are visiting Oslo in October - December 2001, with dates.
Erik Alfsen,
Oslo, 01/10 - 31/12
Bill Arveson,
Berkeley, 29/9 - 01/11
Erik Bedos,
Oslo, 01/10 - 31/12
Etienne
Blanchard, Paris, 27/11 - 5/12
Ola Bratteli,
Oslo, 01/10 - 17/12
Berndt Brenken,
Calgary, 3/11 – 8/11
Roberto Conti,
Erlangen, 01/10 - 14/10
Alfons van
Daele, Leuven, 31/10 - 2/12
Trond Digernes,
Trondheim, 09/10 - 20/12
Dai Evans,
Cardiff, 23/7 - 18/8
Ruy Exel, Sao
Paulo, 01/11 – 10/11
Valentin
Golodets, Kharkov, 08/10 – 14/10
Ilan Hirshberg,
Berkeley, 01/12 – 8/12
Arnoud Frans
Lambert Jacobs, Leuven, 17/09 – 21/12
Palle
Jorgensen, Iowa, 10/7 - 18/8
Lars Kadison,
Gothenburg, 22 – 26/10
Steve
Kaliszewski, Arizona, 02/12 – 23/12
Louis
Labuchagne, Pretoria, 01/11 - 07/11
Marcelo Laca,
Victoria, 04/12 – 09/12
Magnus B.
Landstad, Trondheim, 01/10 - 31/12
Nadia Larsen,
Copenhagen, 31/10 - 08/11 and 08/12 – 14/12
Andrei Lodkin,
Leningrad, 01/11 – 10/11
Mats Molberg,
Trondheim, 02/11 – 16/11
Michael
Müger, Amsterdam, 07/7 - 18/8 and 02/12 - 21/12
Sergey
Neshveyev, Oslo, 01/10 - 31/12
Judith Packer
Jesudason, Singapore and Colorado, 04/11 - 08/11
John Quigg, Arizona,
29/11 – appr. 28/12
Jean Renault,
Orleans, 08/10 - 24/11
Christian Skau,
Trondheim, 15/10 - 20/12
Erling
Størmer, Oslo, 01/10 - 31/12
Kornel
Szlachanyi, Budapest, 22 – 26/10
Lars Tuset,
Oslo, 01/10 - 31/12
Anatoly
Vershik, Leningrad, 03/11 – 09/11
Stanislaw Lech
Woronowicz, Warsaw, 02 – 07/11
Laszlo Zsido,
Rome, 03 – 09/11
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Wednesday 5/9
13:00 - 14:45
Sergey
Neshveyev will continue his lectures on "Popa´s paper on Betti
numbers of II_1 factors"
Wednesday 12
Sept. 14:15 - 16:00 in B62
Sergey
Neshveyev will continue his lectures on "Popa´s paper on Betti
numbers of II_1 factors"
Wednesday 19
Sept. 14:15 - 16:00 in B62
Ola Bratteli will
talk about "Operator Theory in Wavelet Analysis"
Wednesday
3.Oct. 14:15 - 16:00 in B62
Lars Tuset will
talk about "The modular square for quantum SU(2)"
Wednesday 10/10
14:15 - 16:00
Professor
Valentin Golodets, Institute of Low Temperature Physics, Kharkov:
"The
spectrum of completely positive entropy actions of countable amenable
groups"
Monday 15/10
14:15 - 16:00
Professor Bill
Arveson, University of Berkeley
"Generators
for non-commutative dynamics"
Wednesday 17/10
14:15 - 16:00
Professor Jean
Renault, Université d´Orleans
"AF
equivalence relations and their cocycles"
Monday 22/10
14:15 - 16:00
Professor Chris
Skau, University of Trondheim
"Affable
equivalence relations and Cantor dynamical systems"
Wednesday 24/10
14:15 - 16:00
Professor
Kornel Szlachanyi, Institute for Nuclear Research, KFKI, Budapest
"Quantum
groupoids in field theory and quantum field theory"
Abstract. The slight play on words mean the
theory of FIELD extensions in mathematics[Galois, Greither-Pareigis] on the one
hand and the theory of quantum FIELDS in physics [Haag, Doplicher-Roberts] on
the other hand. The emphasis will be on the latter, although both topics need
only weak Hopf algebras as their quantum groupoids, I will at the end talk
about a current preprint with Lars Kadison (QA/0108067).
Thursday 25/10
13:15 – 15:00
Jean Renault
gives an informal seminar on basic aspects of groupoids, Haar-systems and graph
algebras.
Monday 29/10
14:15 - 16:00
Professor Ola
Bratteli, University of Oslo
"A wavelet
index theorem"
Thursday 1/11
13:15 – 15:00
Jean Renault
continues his informal seminar on basic aspects of groupoids, Haar-systems and
graph algebras.
05/11 –
07/11 Workshop on "Operator
algebras and applications" (See below)
Wednesday 14/11
13:15 – 15:00
Professor
Alfons vanDaele. Leuven
"The
Heisenberg Commutation Relations, Commuting Squares and the Haar Measure on
Locally Compact Groups"
Thursday 15/11
13:15 – 15:00
Jean Renault
continues his informal seminar on basic aspects of groupoids, Haar systems and
graph algebras.
Wednesday 21/11
13:15 – 15:00
Arnoud Jacobs,
Leuven
"The
quantum E(2) as an example of a locally compact quantum group"
Thursday 22/11
13:15 – 15:00
Professor Erik
Alfsen, University of Oslo
"On the
use of spectral convex sets in non-commutative probability"
Wednesday 28/11
13:15 – 15:00
Etienne
Blanchard, Paris
"A stellar
analogue of type III von Neumann algebras"
(with E.
Kirchberg and M. Rørdam)
Thursday 29/11
13:15 – 15:00
Professor
Erling Størmer, Oslo
"Entropy
and MASAs of the hyperfinite II_1 – factor”
(with Sergey
Neshveyev)"
Monday 03/12
13:15 – 15:00
Ilan Hirshberg,
Berkeley
"Endomorphisms
of stable continuous-trace C^*-algebras"
Abstract. It is
in some way related to the problem of choosing continuously varying generators
Cuntz algebras, but it doesn't classify those selections, but rather classifies
the obstruction to constructing them. The motivating problem was roughly this
-- if we have a spectrum preserving endomorphism of, say, an algebra of the
form C(X,K) (K being the
compacts), then it is given by a continuous selection of endomorphisms of the
compacts. Each endomorphism of the compacts (subject to a non-degeneracy
condition) is of the form A --> S_1 A S_1^* + ... + S_n A S_n^* for
S_1,...,S_n satisfying the Cuntz relations, but the choice of the S_i's is not
unique. So one question is when can we lift such a continuous selection of
endomorphisms to a continuous selection of the S_i's. The end result gives a complete
and well behaved classification of those endomorphisms, up to unitary
equivalence (composition with an inner automorphism).
Wednesday 05/12
10:15 – 12:00 (NOTE THE TIME)
Professor John
Quigg, Arizona
"Maximal
coactions"
Thursday 06/12
13:15 – 15:00
Marcelo Laca,
Victoria
"Hecke
C*-algebras from number fields"
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SHS Workshop on "Operator algebras and
applications" 5 – 7 November 2001.
Below is the program for the Centre of
Advanced Study workshop "Operator Algebras and Applications" 5-7
November 2001. The talks will take place in the small lecture hall in the
building of the Norwegian Academy of Science and Letters, located at
Drammensveien 78, 0271 Oslo . Just enter through the main entrance at the
front. The workshop starts Monday at 9:00. The main door will be open after
8:30
Each of the
three days of the workshop lunch will be provided free of charge for all the
participants . There will be a workshop dinner at the Academy Monday at 19:00.
to which all the participants are invited.
Most of the
short time workshop participants are lodged in Frogner Hotel (phone 2327 5150),
Frederik Stangs gate 33. To walk to the Academy from there, head down Frederik
Stangs gate (gate = street) for 500 meters towards the fjord, and then
turn right on Drammensveien (veien
= street) Walk along this for 200 meters, past the easily identifiable Russian
embassy on the left side, to the Academy which is located in a stately building
in a garden to the left.
We have put
some information in the reception of Frogner Hotel. Chris Skau is planning a
touristic walk through Oslo from the hotel on Sunday 4 November, starting from
the hotel lobby at 10:30.
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Program
of the workshop.
Monday 5/11
09:00 - 09:45
Anatoly Vershik: "Dynamical systems and C*-Lie-algebras."
10:00 - 10:45
Christian Skau: "Affable equivalence relations and Cantor minimal systems"
11:00 - 11:45
Andrei Lodkin: "Quasicrystallic tilings and their spectra"
12:00 Lunch at
the Academy
14:00 - 14:45
Stanislaw Lech Woronowicz: "Quotients of quantum groups"
15:00 - 15:45
Alfons van Daele: "About the Haar measure on locally compact quantum
groups."
16:00 - 16:45
Erik Bedos: "Amenability and algebraic quantum groups"
19:00
Conference dinner at the Academy
Tuesday 6/11
09:00 - 09:45
Jean Renault: "The Radon-Nikodym problem for AP-equivalence
relations"
10:00 - 10:45
Ruy Exel: "A new look at crossed products by endomorphisms and KMS
states"
11:00 - 11:45
Louis Labuschagne: "A non-commutative theory of composition
operators"
12:00 Lunch at
the Academy
14:00 - 14:45
Berndt Brenken: "Representations of Graph C*-algebras and Endomorphisms"
15:00 - 15:45
Nadia Larsen: "Representations of Hecke algebras, dilations of semigroup
crossed products and applications"
16:00 - 16:45
Magnus B. Landstad: "Hecke subgroups and algebras"
Wednesday 7/11
09:00 - 09:45
Laszlo Zsido: "Non-commutative recurrence theorems"
10:00 - 10:45
Sergey Neshveyev: "Masas in crossed products"
11:00 - 11:45
Erling Størmer: "Entropy in operator algebras and the McMillan
theorem"
12:00 Lunch at
the Academy
14:00 - 14:45
Judith Packer Jesudason: "A Hilbert module approach to wavelet
theory"
15:00 - 15:45
Trond Digernes: "Weyl Systems for Heisenberg Groups and the structure of
their vacuum sectors"
16:00 - 16:45
Erik Alfsen: "On the use of spectral convex sets in non-commutative
probability"
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* Erik Alfsen, Oslo, 1/10 - 31/12
"On the
use of spectral convex sets in non-commutative probability"
* Erik Bedos,
Oslo, 1/10 - 31/12
"Amenability
and algebraic quantum groups"
Ola Bratteli,
Oslo, 1/10 - 17/12
* Berndt
Brenken, Calgary, 3/11 - 8/11
"Representations
of Graph C*-algebras and Endomorphisms"
* Alfons van
Daele, Leuven, 31/10 - 2/12
"About the Haar measure on locally
compact quantum groups."
Abstract: The
theory of locally compact quantum groups, as it exists now, is one where the
existence of the Haar measure is part of the axioms. From a theoretical point
of view, it would be nice to be able to formulate natural axioms from which the
existence of the Haar measure can be proved. Unfortunately, this seems to be
rather difficult.
In practice
however, what is needed is a method to construct the Haar measure in examples.
In some sense, this is more important than an existence proof.
In this talk we
will discuss such a construction procedure and illustrate it to obtain the Haar
measure on the quantum E(2) of S.L. Woronowicz. This Haar measure was first
obtained by S. Baaj.
* Trond
Digernes, Trondheim, 9/10 - 20/12
"Weyl Systems
for Heisenberg Groups and the structure of their vacuum sectors."
Abstract: We
discuss certain models for the irreducible representation of the Heisenberg
group, based on various locally compact abelian groups. In particular, we show
that in certain models the vacuum sector exhibits a fermionic structure. This
phenomenon occurs, for example, if the model based on the 2-adic numbers Q_2.
* Ruy Exel, Sao
Paulo, 1/11 - 10/11
"A new
look at crossed products by endomorphisms and KMS states"
Abstract: I
plan to survey recent developments in the theory of crossed products of
C*-algebras by endomorphism leading up to the computation of KMS states on
Cuntz-Krieger algebras for irreducible aperiodic matrices under an action which
generalizes the usual gauge action.
The talk will consist mainly of the content of the following preprints
by the author, all of which are available from the preprint server at
xxx.lanl.gov:
1) A new look at the crossed-product of
a C*-algebra by an endomorphism,
math.OA/0012084,
2) Crossed-products by finite index
endomorphisms and KMS states,
math.OA/0105195,
3) KMS states for generalized gauge
actions on Cuntz-Krieger algebras
(An application of
the Ruelle-Perron-Frobenius Theorem),
math.OA/0110183.
* Louis
Labuschagne, Pretoria, 1-7/11
"A
non-commutative theory of composition operators"
Abstract: We
briefly survey some basic principles that underlie the theory of composition
operators on classical $H^p$, $L^p$, and $C^(p)$-spaces before indicating how
the theory may be extended to non-commutative analogues of these spaces. The
desirability of such an extension of course lies in its potential as a tool for
significantly refining "non-commutative modelling". In closing we discuss the progress that
has been made to date and also highlight some significant challenges that
remain.
* Magnus B.
Landstad, Trondheim, 1/10 - 31/12
"Hecke
subgroups and algebras"
* Nadia Larsen,
Copenhagen, 31/10 - 8/11
"Representations
of Hecke algebras, dilations of semigroup crossed products and
applications"
Abstract: We
consider a family of Hecke C^*-algebras which can be realised as semigroup
crossed products. By dilating representations of the semigroup crossed product
we can show that the category of representations of the Hecke algebra is
equivalent to the category of continuous unitary representations of a totally
disconnected locally compact group. We use this point of view to give a quick
proof of the self-duality of the adele group and of similar groups. This is
joint work with Iain Raeburn.
* Andrei
Lodkin, Leningrad, 1/11 to approximately 12/11
"Quasicrystallic
tilings and their spectra"
Abstract: A
tiling of the space is called quasicrystallic if it has discrete diffusion
spectrum. A tiling (or the related countable Delone set) is of this kind if it
can be obtained by the projection scheme (then the spectrum can be easily
found). We shall speak mostly about examples of such tilings with the emphasis
on tilings of substitutional origin.
Mats Molberg,
Trondheim, 2 - 16/11
* Sergey
Neshveyev, Oslo, 1/10 - 31/12
"Masas in
crossed products."
Abstract: We
shall discuss masas in crossed products of finite von Neumann algebras by
abelian groups, their normalizers and conjugacy problem.
* Judith Packer
Jesudason, Singapore and Colorado, 4-8/11
" A
Hilbert module approach to wavelet theory".
* Jean Renault,
Orleans, 8/10 - 24/11
"The
Radon-Nikodym problem for AP-equivalence relations"
Abstract:
Approximately proper (AP) equivalence relations occur naturally in the theory
of AF-C$^*$-algebras and in the theory of expansive local homeomorphisms. The
study of their C$^*$-algebras, which include AF-C$^*$-algebras and the
commutative C$^*$-algebras, is very similar to the theory of AF-C$^*$-algebras.
The core of the talk will be about the Radon-Nikodym problem, which is to find
all the quasi-invariant measures admitting a given cocycle as their
Radon-Nikodym derivative. We shall give applications to KMS states and to the
thermodynamical formalism.
* Christian Skau,
Trondheim, 15/10 - 20/12
"Affable
equivalence relations and Cantor minimal systems"
* Erling
Størmer, Oslo, 1/10 - 31/12
"Entropy
in operator algebras and the McMillan theorem"
Lars Tuset,
Oslo, 1/10 - 31/12
* Anatoly
Vershik, Leningrad, 3/11 - 9/11
"Dynamical
systems and C*-Lie-algebras."
Abstract: For
any measure preserving automorphism or flow we define in a canonical way a
graded Lie algebra. This is similar to the well-known construction of the
associative C*-algebras (cross-products) corresponding to dynamical systems.
That algebra is a graded Lie algebra with a continuum root system and has very
important central extensions. It is a continuum analog of Kac-Moody Lie
algebras and representations of it supposedly gives new tools in algebraic
theory of dynamical systems. The simplest example corresponding to the
irrational rotation is the so called sine algebra.
* Stanislaw
Lech Woronowicz, Warsaw, 2 - 7/11
"Quotients
of quantum groups"
* Laszlo Zsido,
Rome, 3 - 9/11
"Non-commutative
recurrence theorems"
Abstract: I
think to present versions of Khintchine's and Furstenberg's recurrence theorems
in the non-commutative framework of operator algebras. I plan to discuss with
particular care the recurrence properties of weakly mixing C*-dynamical
systems. The presented results were obtained jointly with C. Niculescu and A.
Stroh.
Students from
Oslo who will participate:
Sindre Duedahl
Arnaud Jacobs
Kjetil
Røysland