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{\large
\vskip -3cm
\hskip 6cm {\sl\bf Book of Abstracts for the 3rd Conference of Settat}

\hskip 6cm {\sl\bf on Operator Algebras and Applications,}

\hskip 6cm {\sl\bf November 1--5, 2011}

}
\vskip 3cm

\begin{enumerate}
\item
\noindent {\bf ({\bf Opening Ceremony})}:\\
\noindent Mohammed Akkar (University Bordeuax, France)\\
\noindent {\bf Title}: Pouvoir, plaisir et efficacit� des math�matiques\\
%( Conf�rence inaugurale par M. Akkar)
\noindent  {\bf Abstract}:
Introduction: Prix Nobel 2011 \`a 3 astrophysiciens (Acc\'el\'eration de l'expansion de l'univers)\\
\noindent I.	Le pouvoir des Math\'ematiques.\\
Les math\'ematiciens sont des explorateurs. Leur objectif: r\'esoudre des probl\`emes (les leurs et ceux des autres sciences).\\
\noindent 1$^o$) Lien avec l'Informatique.\\
\noindent 2$^o$) Lien avec la finance moderne et les march\'es.\\
\noindent 3$^o$) Math\'ematiques et codes secrets.\\
\noindent 4$^o$) Lien avec la physique (surtout th\'eorique).\\
\noindent II. Plaisir et n\'ecessit\'e\\
\noindent  III.	Outil incontournable dans les sciences modernes:
Dont: la M\'et\'eorologie, les T\'el\'ecommunications et les R\'eseaux, la M\'edecine et les Sciences du Vivant, le traitement d'images, d\'etection (ou anti-) radar, probl\`emes ADN, transport a\'erien, trafic Internet, codes correcteurs, exploration g\'eologique, archivage des vestiges arch\'eologiques, imagerie m\'edicale ou industrielle (reconstitution de surfaces \`a partir de quelques points), ...\\
\noindent IV. Les math\'ematiques dans le Monde, en France et au Maroc.\\
\noindent V. L'\^age d'or des math\'ematiques et de la langue arabes\\
Conclusion: l'enseignement des math\'ematiques aujourd'hui au Maroc

Bibliographie

\noindent  1.	M. Akkar, L'\^age d'or des sciences et de la langue arabes, Conf\'erence � l'Alliance Fran�aise de Safi, 2009.\\
\noindent  2.	L'\^Age d'or des sciences arabes, Actes Sud / Institut du Monde Arabe, oct. 2005\\
\noindent 3.	La Recherche (Dossiers), Le Pouvoir des Math\'ematiques, Novembre 2009\\
\noindent 4.	Maths et Finance, HS N$^o$ 32, Tangente, Paris 2008\\
\noindent 5.	L'explosion des Math\'ematiques, SMF-SMAI, Juillet 2002\\
\noindent 6.	La Recherche en Informatique, Le Courrier du CNRS, Dossiers scientifiques.\\
\noindent 7.	La magie des nombres, Sciences et Avenir, HS, 2009\\
\noindent 8.	L'origine du monde, le Nouvel Observateur, HS, 2011.\\
\noindent 9.	Les valeurs de la science ;: beaut\'e des math\'ematiques et intelligibilit\'e du monde, Sciences et Avenir HS , Novembre 2005.


\newpage

\centerline{\bf\Large Talks}

\bigskip


\bigskip
\item
\noindent {\bf Speaker}: Mohammed Akkar (University Bordeuax, France)\\
\noindent {\bf Title}: Id\'ees g�niales et f\'econdes de Lucien Waelbroeck
en th�orie spectrale et calcul fonctionnel.\\
\noindent  {\bf Abstract}:
%( Mohamed Akkar, Colloque Settat, Novembre 2011)
(Cette conf\'erence est prononc\'ee pour rendre hommage
\`a Lucien Waelbroeck, math\'ematicien belge de l'U.L.B
pour son �uvre en g\'en\'eral et pour les travaux
des jeunes chercheurs marocains qu'il a dirig\'es)\\
Note historique: Lucien Waelbroeck est n\'e \`a Gen\`eve en 1929 et mort \`a Bruxelles en 2009. Il a obtenu sa Licence de Math\'ematiques \`a l'U.L.B.\ en 1950 et une bourse en 1953-54 pour s\'ejourner au Coll\`ege de France \`a Paris aupr\`es de Jean Leray pour pr\'eparer sa th\`ese de doctorat. Il a soutenu cette derni\`ere en 1954 sur le calcul symbolique dans les alg\`ebres commutatives et en 1960 il soutint sa th\`ese d'habilitation-agr\'egation sur l'\'etude spectrale  des alg\`ebres compl\`etes. Il devint professeur \`a l'U.L.B.\ en 1962, titulaire de la chaire d'Analyse Math\'ematique. Ses travaux de recherches les plus importants sont all\'es dans trois directions: la th\'eorie spectrale et le calcul fonctionnel holomorphe dans les alg\`ebres, les espaces bornologiques et les espaces quotients. Il a dirig\'e de nombreux chercheurs dont la majorit\'e sont des marocains parmi lesquels je peux citer (avec s�rement des oublis): Hemdaoui, Berkani, Aqzzouz, Raouyane, Houimdi, Anane El Idrissi,..., D'autres sans travailler avec lui ont b\'en\'efici\'e de ses id\'ees: Akkar, Chidami, Abdelali, Tajmouati, El Harti, Arroub ...

\noindent I.\	Calcul fonctionnel holomorphe et th\'eorie spectrale dans les alg\`ebres.

Id\'ees de Walbroeck dans ses deux th\`eses et ses articles, ainsi que dans ses livres (Lectures Notes Springer)\\
Travaux de ses \'el\`eves marocains\\
Travaux de ses autres \'el\`eves\\
Travaux inspir\'es par son �uvre au Maroc et ailleurs\\
\noindent II.\ Espaces bornologiques (espaces \`a born\'es)\\
Travaux de ses \'el\`eves marocains\\
Travaux de ses autres \'el\`eves\\
Travaux inspir\'es par son �uvre au Maroc et ailleurs\\
\noindent III.\ Espaces quotients: les q-espaces et les q-alg\`ebres.\\
Travaux de ses \'el\`eves marocains\\
Travaux de ses autres \'el\`eves\\
\noindent IV.\	Illustrations des id\'es f\'econdes:\\
1$^o$)\  Les \'el\'ements r\'eguliers\\
2$^o$)\  Le trick d'Arens-Calderon\\
3$^o$)\  Calcul fonctionnel holomorphe de dimension infinie\\

{\footnotesize
BIBLIOGRAPHIE\\
\noindent[1] M. Akkar, Th\'eorie spectrale d'op\'erateurs fortement born\'es, S\'eminaire Choquet, 1972-73, N$^o$ 2, Paris.\\
\noindent [2] M. Akkar, Structure bornologique des A.L.M.C., C.R.A.S. Paris, T.279, 1974, s\'erie A, p ; 941-944\\
\noindent [3] M. Akkar, Fonctions enti\`eres et th\'eor\`emes de Banach-Steinhaus, S\'eminaire Choquet, 1975-76, Paris\\
\noindent [4] M. Akkar, Etude spectrale et structures d'alg\`ebres topologiques et bornologiques compl\`etes, Th�se d'\'etat, 1976, Bordeaux.\\
\noindent [4bis] M. Akkar, Calcul fonctionnel holomorphe pour un \'el\'ement non r\'egulier, Afrika Matematika, Vol 1, N$^o$ 1, 1978, pp. 19-33.\\
\noindent [5] G.R. Allan, A spectral theory for locally convex algebras, Proc. London Math. Soc. 3, 15, 1965, p. 399-421.\\
\noindent [6]  B. Aqqzouz, les ?-produits dans la cat\'egorie des quotients bornologiques et applications, Th\`ese U.L.B., 1987-88\\
\noindent [7] R. Arens, A.P. Calderon, Analytic functions of several Banach algebras elements, Ann. of Math. 62, 1955.\\
\noindent [8] H. Arroub, C.F.H. multiforme et sph\`ere de Riemann, Th\`ese Rabat 1986.\\
\noindent [9] H. Arroub, Divers calculs fonctionnels dans les alg\`ebres quotients et applications. Th\`ese d'\'etat, Rabat 1997.\\
\noindent [10] H. Arroub, Calcul fonctionnel harmonique dans une alg\`ebre de Banach involutive quotient. Bull.\ Belg. Math. Soc. 3, 1996, p. 521-535.\\
\noindent [10bis] H. Arroub, Applications du C.F.H. quotient, Bull. Belg. Math. Soc. 3, 1996,        p.595-602\\
\noindent [11]   A.  Beddaa, Th\'eor\`emes du type Gelfand-Naimark dans les alg\`ebres topologiques ou bornologiques, Th�se d'\'etat, 1994.\\
\noindent [12] M. Berkani,  Le calcul fonctionnel bas\'e sur la transform�e de Fourier (Helton-Howe) Th\`ese U.L.B. 1988-89.\\
\noindent [13]  A. Blali, Th\`eses de 3\`eme cycle et \'etat et plusieurs articles. Sur les fonctions enti\`eres dans les alg\`ebres topologiques ou bornologiques, Rabat 1986, F�s, 1998 et th\`ese d'\'etat F\`es.\\
\noindent [14] L. Bouras, Calculs fonctionnels holomorphe et harmonique dans des alg\`ebres non Banach, Th\`ese, Bordeaux.\\
\noindent [15]  N. Bourbaki, Th\'eories spectrales, Hermann, Paris 1967.\\
\noindent [16]  H. Buchwalter, Espaces vectoriels bornologiques, Publ. D�p. Math. Univ. Lyon, 1965, p. 1-53.\\
\noindent [17] H. Cartan, Th\'eorie spectrale des C-alg\`ebres commutatives (d'apr\`es L. Waelbroeck), S\'eminaire Bourbaki, 1955-56.\\
\noindent [18] O. H. Cheikh, Etude de certaines alg\`ebres topologiques ou bornologiques, Rabat, 1998.\\
\noindent [19]  M. Chidami, Calcul fonctionnel holomorphe de dimension infinie, Th\`ese Bordeaux 1977.\\
\noindent [20] M. Chidami, Calcul fonctionnel holomorphe de dimension infinie et prolongement des caract�res, Th\`ese d'\'etat, Rabat 1992\\
\noindent [21]  M. Chidami \& R. El Harti, Calcul fonctionnel holomorphe de dimension finie dans les A.L.M.C.\\
\noindent [22]  I. Cnop, Spectral study of holomorphic functions with bounded growth, Annales de l'Institut Fourier, Grenoble 1972, p; 239-309.\\
\noindent [23]  M. El Azhari, Continuit� des caract\`eres et des formes positives sur certaines alg\`ebres, Th\`ese d'\'etat, Rabat, 1994.\\
\noindent [24]  R.\ El Harti, Calcul fonctionnel holomorphe dans les alg\`ebres compl\`etes, Th\`ese d'\'etat, Rabat 1993.\\
\noindent [25]  R.\ El Harti, Banach Algebras with trivial cohomology, First Advanced course in Operator theory and complex analysis, University of Seville, 2004.\\
\noindent [26]  A. El Idrissi, Th\'eorie de la cat\'egorie des quotients d'espaces de Julia et applications,
Th\`ese U.L.B. Belgique, 1991-92.\\
\noindent [27] A. El Kinani, Calcul harmonique dans les alg\`ebres de Banach involutives et Applications, Th\`ese d'\'etat, K\'enitra, 1994.\\
\noindent [28]   J.P. Ferrier, Spectral theory and complex analysis, North-Holland, Mathematical Studies, 4, Amsterdam, 1973.\\
\noindent [29] M. Hemdaoui, Calcul symbolique et Op\'erateur de Laplace, Th\`ese U.L.B. 1986-87.\\
\noindent [30] H. Hogb\'e-Nlend, Th\'eorie des bornologies et applications, Springer Verlag, L.N. in Math. 213, 1971.\\
\noindent [31]  H. Hogb\'e-Nlend, Les bornologies et l'Analyse Fonctionnelle, North-Holland, 1976.\\
\noindent [32]  Ch. Houzel, S\'eminaire Banach, L.N.\ in Mathematics, 277, Springer Verlag, 1972.\\
\noindent [33] El H. Illoussamen, Continuit\'e automatique des d\'erivations et des op\'erateurs pr\'eservant la disjonction, Th\`ese d'\'etat, Rabat 1996.\\
\noindent [34]  H. Kemmoun,  Contributions aux alg\`ebres localement A-convexes, Th\`ese, 1986\\
\noindent [35]  A. Lazraq-Khlass, Structure et th\'eorie spectrale d'alg\`ebres topologiques (Ij)-adiques, Th\`ese d'\'etat, Rabat, 1999.\\
\noindent [36]  A. Medbouhi, Calculs fonctionnels holomorphe et harmonique dans les alg\`ebres de Jordan-Banach non commutatives quotients et applications. Th\`ese, F\`es, 2002.\\
\noindent [36bis]  A. Medbouhi et A. Tajmouati, Bull. Belg. Math. Soc. 3, 2002\\
\noindent [37]  Ch. Nacir, Sur les limites inductives localement convexes ou bornologiques convexex d'alg\`ebres de Fr\'echet, Th\`ese d'\'etat, Rabat 0995.\\
\noindent [37bis] Ch. Nacir, Sur la vacuit\'e du spectre d'un element d'une algebra LF, Periodica Mathematica Hungarica, Vol. 31, 3, 1995.\\
\noindent [38]  G. No�l, Produit tensoriel et Platitude des Q-espaces, Bull. Soc. Math. Belgique, 22, 1970\\
\noindent [39]   L. Oubbi, A-convexit\'e dans les alg\`ebres de fonctions, Th\`ese d'\'etat K\'enitra, 1994.\\
\noindent [40]  M. Oudadess, Functional bounddness of some M-complete m-convex algebras, Bull. Greek Math.  Soc.  39  (1997), 17--20.\\
\noindent [40bis]  M. Oudadess, Bounded structures of uniformly A-convex algebras, Banach Journal Math. Anal. Volume 3, Number 1 (2009), 19-27\\
\noindent [41] A. Ouhmidou, Calcul fonctionnel harmonique et analytique reel dans les *-abmc compl\`etes et applications, Th\`ese Bordeaux 1997.\\
\noindent [42] M. Raouyane, Alg\`ebres quotients, Th\`ese U.L.B.\\
\noindent [43] J. Sebastio E Silva, Sur le calcul symbolique d'op\'erateurs permutables \`a spectre vide ou non born\'e, Ann. di Math. P. e Appl. 14, 1962, p.  219-276.\\
\noindent [44] A. Tajmouati, Sur les diviseurs topologiques et bornologiques de z\'ero, la bornitude automatique des op\'erateurs lin\'eaires et les multiplications dans certaines alg\`ebres non associatives, Th\`ese d'\'etat, Rabat, 1995.\\
\noindent [45] J.L. Taylor, The analytic functionnal calculus for several commuting operators, Acta Mathematica 125, 1970, p.1-32.\\
\noindent [46]  F.-H. Vasilescu, Spectral theory in Quotient Fr\'echet Spaces I \& II, Revue Roumaine de Math. P. et A. 32, 1987, p.561-571 et J. Operator Theory 21, 1989, p.47-52\\
\noindent [47] L. Waelbroeck, Le calcul symbolique dans les alg\`ebres commutatives, J. Math. Pures et Appl. 33, 1954\\
\noindent [48] L. Waelbroeck, Etude spectrale des alg\`ebres completes, Acad\'emie Royale de Belgique, Mem. Classe des sciences , 1960\\
\noindent [49] L. Waelbroeck, Topological vector spaces and algebras, L.N. In Math., 230, Springer-Verlag, 1971.\\
\noindent [50]  L. Waelbroeck, Bornolical Quotients with the collaboration of Guy No�l, Acad�mie Royale de Belgique, Classe des sciences , 2005.

}

\bigskip
\item
\noindent {\bf Speaker}: Ahmed Al-Rawashdeh (Dept.\ of Mathematical Sciences, UAEU,
Al-Ain, Abu Dhabi)\\
\noindent {\bf Title}: On Certain Projections of C*-Matrix Algebras\\
\noindent {\bf Abstract}: H. Dye defined the projections $P_{i,j}(a)$ of a
$C^*$-matrix algebra by
\begin{eqnarray*}
P_{i,j}(a) &=& (1+aa^*)^{-1}\otimes E_{i,i} + (1+aa^*)^{-1}a \otimes
E_{i,j}\\
 &+& a^*(1+aa^*)^{-1} \otimes  E_{j,i} +
a^*(1+aa^*)^{-1}a\otimes E_{j,j},
\end{eqnarray*}
and he used it to show that in the case of factors not of type
$I_{2n}$, the unitary group determines the algebraic type of that
factor. We study these projections and we show that in
$\mathbb{M}_2(\mathbb{C})$, the set of such projections includes all
the projections. For infinite $C^*$-algebra $A$, having a system of
matrix units, including the Cuntz algebra $\mathcal{O}_n$, we have
$A\simeq \mathbb{M}_n(A)$. M. Leen proved that in a simple, purely
infinite $C^*$-algebra $A$, the $*$-symmetries generate
$\mathcal{U}_0(A)$. We revise and modify Leen's proof to show that
part of such $*$-isometry factors are of the form $1-2P_{i,j}(\omega
),\ \omega \in  \mathcal{U}(A)$. In simple, unital purely infinite
$C^*$-algebras having trivial $K_1$-group, we prove that all
$P_{i,j}(\omega )$ have trivial $K_0$-class. In particular, if $u\in
\mathcal{U}(\mathcal{O}_n)$, then $u$ can be factorized as a product
of $*$-symmetries, where eight of them are of the form
$1-2P_{i,j}(\omega )$.


\bigskip
\item
\noindent {\bf Speaker}: Pere Ara (Universitat Aut\`onoma de Barcelona, Spain)\\
\noindent {\bf Title}: $(m,n)$-dynamical systems and their C*-algebras\\
\noindent {\bf Abstract}: Given positive integers $n$ and $m$, we consider dynamical systems in
which $n$ copies
of a topological space is homeomorphic to $m$ copies of that same space.
 The universal such system is shown to arise naturally from the study of a
C*-algebra we denote by $\mathcal O_{m,n}$, which in turn is obtained as a
quotient of the
C*-algebra $L_{m,n}$ of a certain separated graph, a process meant to
transform
the generating set of partial isometries of $L_{m,n}$ into a tame set.
 Describing $\mathcal O_{m,n}$ as the crossed-product of the universal
$(m,n)$-dynamical system by a partial action of the free group
$\mathbb F_{m+n}$, we show that $\mathcal O_{m,n}$ is not exact when $n$
and
$m$ are both greater than or equal to 2, but the corresponding reduced
crossed-product,  denoted $\mathcal O^r_{n,m}$,  is shown to be exact and
non-nuclear.
 Still under the assumption that $n, m\geq 2$, we prove that the partial
action
of $\mathbb F_{m,n}$ is topologically free and that $\mathcal O^r_{m,n}$
satisfies property (SP) (small
projections). Joint work with R.\ Exel and T.\ Katsura

%\bigskip
%\item
%\noindent {\bf Speaker}:  Huzihiro Araki (Kyoto University, Japan)\\
%\noindent {\bf Title}: \\
%\noindent {\bf Abstract}:



\bigskip
\item
\noindent {\bf Speaker}: Roseli Arbach (UNESP - Ilha Solteira, Brazil)\\
\noindent {\bf Title}: C*-algebra of Regulated Functions with values in $M_{2}(\mathbb{R})$\\
\noindent {\bf Abstract}: In this paper we deal with the notion of regulated functions with values in a
C$^{*}$-algebra $\cal A $, we prove some results and present examples using a special bi-dimensional C$ ^{*} $-algebra of triangular matrices.



%In this paper we deal with the notion of regulated functions with values in a C$ ^{*} $-algebra $ \cal A $, we %prove some results and present examples using a special bi-dimensional C$^{*} $-algebra of triangular matrices.



%\bigskip
%\item
%\noindent {\bf Speaker}: Joseph Ball (Verginia Tech University, USA)\\
%\noindent {\bf Title}: \\
%\noindent {\bf Abstract}:


\bigskip
\item
\noindent {\bf Speaker}: Mashhour Bani Ata (Department of Mathematics-Aladeeliyah, Kuwait)\\
\noindent {\bf Title}: Non -Associative Central Division Algebras  of order $q^4$,and Matrix Representations\\
\noindent {\bf Abstract}: The aim of this talk is to classify  the non-associative division
algebras of order $q^4$ with center Fq, admitting a Klein four group of automorphisms acting freely.



\bigskip
\item
\noindent {\bf Speaker}: Viacheslav Belavkin (University Nottingham, UK)\\
\noindent {\bf Title}: An Introduction into Modular Theory of Entanglement and Information\\
\noindent {\bf Abstract}: A noncommutative algebraic approach to unified
classical and quantum information theory is given. An operational meaning of
entanglement as specifically quantum encoding is disclosed. The general
relative entropy as information divergence is introduced and three most
important types of relative information, namely, Araki-Umegaki (A-type) and
of Belavkin-Staszewski (B-type) and the thermodynamical (C-type) are shown.
The true quantum entropy different from the von Neumann semiquantum entropy
is introduced and the proper quantum conditional entropy is showen. The
general quantum mutual information via entanglement is defined and the
corresponding types of quantum channel capacities as the supremum via the
generalized encodings are formulated. The additivity problem for quantum
logarithmic capacities for the products of arbitrary quantum channels under
the appropriate constraints on encodings is discussed. It is proved that the
true quantum capacity, which is achieved on the standard entanglement as the
optimal quantum encoding, reclaims the additivity property of the
logarithmic quantum channel capacities via the entanglement on the products
of quantum input states. This earlier obtained by V. P. B. result for
quantum logarithmic information of A-type is extended to to any type of
quantum information.


\bigskip
\item
\noindent {\bf Speaker}: Martin Bohata and Jan Hamhalter (Czech Technical University in Prague, Czech Republic)\\
\noindent {\bf Title}: Star order on operator algebras\\
\noindent {\bf Abstract}: A number of interesting orders have been studied for matrix algebras.
Recently, one of  them, called the star order,  was investigated for
infinite-dimensional Hilbert-space operators in [1]. The star order,
$\le_\ast$, is  defined for bounded operators $a$  and $b$ acting on a
Hilbert space as follows: $a\le_\ast b$ if $a^\ast a=a^\ast b$ and
$aa^\ast=ba^\ast$. We continue this line of the research by studying an
interesting relationship between the structure of $C^\ast$-algebras and
properties of the star order. In this respect we show, for example, that a
unital $C^\ast$-algebra is infinite if, and only if, there is a partial
isometry $u_1$ and coisometry $u_2$ such that $u_1\le_\ast u_2$,
$u_1\not=u_2$, and $u_1u_1^\ast=u_2^\ast u_2$ [2]. Then we contribute to
the well known infimum problem by showing that two elements of abelian
 $C^\ast$-algebra $A$ have always  infimum in the star order provided that
the spectrum of $A$ is locally connected or extremely disconnected [2].
(This  is a consequence of our analysis of the star order on more general
function algebras of  topological spaces.) Finally,  we study nonlinear
preserves of the star order for von Neumann algebras. Let $\varphi$ be a
 continuous (not necessarily linear) bijection  between normal parts of von
Neumann algebras $A$ and $B$, where $A$ has no Type $I_2$ direct summand.
Suppose that $\varphi$  preserves the star order in both directions. Then
we show that, under mild condition on the restriction of $\varphi$ to the
one-dimensional space generated by the unit of $A$, $\varphi$ is of the
form $\varphi(x)=z\psi(g(x))$, where $z$ is a central invertible element of
$B$, $\psi:A\to B$ is a $\ast$-Jordan isomorphism and
$g:\mathbb{C}\rightarrow\mathbb{C}$ is a bijective continuous function.
This result generalizes the description of nonlinear preservers of Gudder
order on self-adjoint parts of Type I factors [3].
An important ingredient of the proof is an interesting application of the
Dye's Theorem and
Generalized Gleason's Theorem (see [4, Chapter 8]).
We discuss various ramifications of these results and their generalizations
to  Jordan von Neumann algebras (JBW algebras).


\begin{thebibliography}{9}

\bibitem{} J. Antezana, C. Cano, I. Musconi, and D. Stojanoff: A note on
the star order in Hilbert spaces, Lin. Multilin. Alg. {\bf 58} (2010),
1037-1051.

\bibitem{} M. Bohata: Star order on operator and function algebras, Publ.
Math. Debrecen {\bf 79/1-2} (2011), 211-229.

\bibitem{} G. Dolinar and L. Moln\'{a}r: Maps on quantum observables
preserving the Gudder order, Rep. Math. Phys. {\bf 60} (2007), 159-166.

\bibitem{} J. Hamhalter: Quantum Measure Theory, Kluwer Academic
Publishers, Dordrecht, 2003.

\end{thebibliography}

\bigskip
\item
\noindent {\bf Speaker}: Abdelhamid Boussejra (University Ibn Toufail, Morocco)\\
\noindent {\bf Title}: The Hua operators on homogeneous line bundle on Bounded Symmetric Domains of Tube Type\\
\noindent {\bf Abstract}: Let $\mathfrak{D}$ be a bounded symmetric domain of tube type. We show that the image of the Poisson transform on the degenerate principal series representation attached to the Shilov boundary of $\mathfrak{D}$ is characterized by a covariant differential operator on a homogeneous line bundle on $\mathfrak{D}$.


%\bigskip
%\item
%\noindent {\bf Speaker}: Marek Bozejko (University of Wrocaw, Poland)\\
%\noindent {\bf Title}: \\
%\noindent {\bf Abstract}:

\def\gp#1{\langle #1 \rangle}

\bigskip
\item
\noindent {\bf Speaker}: Victor Bovdi (University of Debrecen, Hungary)\\
\noindent {\bf Title}: Group rings whose group of units is  hyperbolic\\
\noindent {\bf Abstract}: Let $(X, \rho)$ be a metric space with  metric $\rho$. For  any $a,b,c \in  X$,
the Gromov product $\gp{b,c}_a$ of $b$ and $c$  with respect to $a\in X$  is defined as
\[
\gp{b,c}_a =\frac{1}{2}\Big(\rho (b,a)+\rho(c,a)-\rho(b,c)\Big).\textstyle
\]
The metric space is called $\delta$-hyperbolic ($\delta\geq  0$) if
\[
\gp{a,b}_d\geq \min\big\{ \gp{a,c}_d,\gp{b,c}_d\big\}-\delta \qquad(a,b,c,d\in X).
\]
Let $G$ be a finitely generated group and let $S$ be a finite set of generators of $G$. The Cayley graph
$\mathfrak{C}(G,S)$ of the group $G$ with respect to the set  $S$ is the metric
graph whose vertices are in one-to-one correspondence with the elements of $G$.
An edge  (labeled by $s$)   joins  $g$ to $gs$ for some $g\in G$ and  $s\in S$.
The group $G$ is called  {\it hyperbolic} (according to M.~Gromov) if its Cayley graph
$\mathfrak{C}(G,S)$ is a $\delta$-hyperbolic metric space for some $\delta\geq 0$.
It is well known  that this definition does not depend on the
choice of the generating set $S$.

The  following   question can be posed: When is  the group of  units $U(KG)$ of the group
ring $KG$ of a group $G$ over the commutative ring $K$ with unity  hyperbolic.

In certain papers of E.~Iwaki, E.~Jespers, O.~Juriaans, A.~Souza Filho, I.B.~Passi and D.~Prasad
this problem was solved for several particular cases.

In my talk we give a general  solution of this problem.

%\bigskip
%\item
%\noindent {\bf Speaker}: Nathanial P. Brown (The Pennsylvania State University, USA)\\
%\noindent {\bf Title}: \\
%\noindent {\bf Abstract}:


\bigskip
\item
\noindent {\bf Speaker}: Emmanuel Chetcuti and Jan Hamhalter (University of
Malta, Malta)\\
\noindent {\bf Title}: Convergence of non-commutative measures and absolute continuity\\
\noindent {\bf Abstract}: The object of the present note is to give an overview of some recently
obtained results related to the  extension of classical convergence
theorems to non-commutative set-up.  We shall mainly focus on the notion
of absolute continuity of non-commutative measures and discuss the
possible extensions of the Vitali-Hahn-Saks Theorem and the Brooks-Jewett
Theorem to operator algebras.  Our investigation is mainly based on the
results obtained in \cite{CH1,CH2,CH3,H}.  Let us mention that other
significant contributions can be found also in \cite{BSW1,BSW2,BW,SW}
where a stronger form of absolute continuity is considered.  It will be
seen that although some results extend without injury, others cannot have
a non-commutative analogue. It will be shown, for example, that the
Vitali-Hahn-Saks Theorem for von Neumann algebras is valid when one
considers positive measures or when one assumes that the controlling
measure is a faithful one.  The transition to signed measures is not
priceless however.  In fact, it will be shown that the finite von Neumann
algebras are the only algebras for which the Vitali-Hahn-Saks Theorem
holds. In addition, we shall characterize those $C^\ast$-algebras for
which the Brook-Jewett Theorem holds as follows:  A $C^\ast$-algebra
satisfies the Brooks-Jewett Theorem if, and only if, it is a Grothendieck
space and each of it's irreducible representation is finite-dimensional.
\providecommand{\bysame}{\leavevmode\hbox
to3em{\hrulefill}\thinspace}
\begin{thebibliography}{4}
\bibitem{BSW1} J.~K.~Brooks, K.~Sait\^o and J.~D.~M.~Wright, \emph{When
absolute continuity on $C^\ast$-algebras is automatically uniform}, Q. J.
Math. {\bf 55} (2004),  31?-40.

\bibitem{BSW2} \bysame, \emph{Operators on $\sigma$-complete
$C^*$-algebras}, Q. J. Math. {\bf 56} (2005),  301?-310.

\bibitem{BW}  J.~K.~Brooks and J.~D.~M.~Wright, \emph{Convergence in the
dual of a $\sigma$-complete $C^*$-algebra}, J. Math. Anal. Appl. {\bf 294}
(2004), 141?-146.

\bibitem{CH1} E.~Chetcuti and J.~Hamhalter, \emph{Vitali-Hahn-Saks theorem
for vector measures on operator algebras},  Quart. J. Math. {\bf 57}
(2006), 479--493.

\bibitem{CH2} \bysame, \emph{Noncommutative Vitali-Hahn-Saks Theorem holds
precisely for finite $W^\ast$-algebras}, Quart. J. Math.  {\bf 60} (2009),
45--51.

\bibitem{CH3} \bysame, \emph{A noncommutative Brooks-Jewett Theorem}, J.
Math. Anal. Appl. {\bf 355} Issue 2 (2009),  839--845.

\bibitem{H} J.~Hamhalter, \emph{Absolute continuity and non-commutative
measure theory}, Int. J. Theor. Phys. {\bf 49} (2010), 3139--3145.

\bibitem{SW} K.~Sait\^o and J.~D.~M.~Wright, \emph{Absolute continuity on
$C^\ast$-algebras}, Q. J. Math. {\bf 61} (2010),  135?-140

\end{thebibliography}
%%%%



%\bigskip
%\item
%\noindent {\bf Speaker}: Raul Curto (University of Iowa, USA)\\
%\noindent {\bf Title}: \\
%\noindent {\bf Abstract}:

%\bigskip
%\item
%\noindent {\bf Speaker}: Siegfried Echterhoff (University Munster, Germany)\\
%\noindent {\bf Title}: \\
%\noindent {\bf Abstract}:

%\bigskip
%\item
%\noindent {\bf Speaker}: El Houcein El Abdelaoui (University Rouan, France)\\
%\noindent {\bf Title}: \\
%\noindent {\bf Abstract}:


\bigskip
\item
\noindent {\bf Speaker}: Jean Esterle (University of Bordeaux I, France)\\
\noindent  {\bf Title} Normability of algebras of power series, prime ideals,
and discontinuous algebra norms on ${\cal C}(K)$\\
\noindent {\bf Abstract}: The existence of discontinuous algebra norms on  ${\cal C}(K),$ $K$ infinite compact space, known as Kaplansky's problem, is not a decidable question. Such discontinuous norms do exist if the continuum hypothesis is assumed (this is related to the normability, in ZFC, of a "universal" algebra of power series).
In the other direction there are models of set theory, including the axiom of choice and Martin's axiom, in which all algebra norms on ${\cal C}(K)$ are equivalent to the usual norm $f \to \Vert f \Vert_K:=\mbox{max}_{t\in K}\vert f(t)\vert.$\\
It is well-known that if $p$ is a discontinuous algebra norm on ${\cal C}(K)$ then every $p$-closed ideal of ${\cal C}(K)$ is the intersection of the family of all $p$-closed {\bf prime} ideals which contain it, and that every chain of $p$-closed ideals is well-ordered with respect to inclusion. For some infinite compact spaces, as the Alexandroff or the Stone-Cech compactification of ${\mathbf N},$ it is easy to see that the set of all minimal $p$-closed ideals must be finite. So for these compact spaces the set of nonmaximal $p$-closed prime ideals is a finite union of well-ordered chains. Conversely, if the continuum hypothesis is assumed, it is possible for such a compact space $K$, given a finite union ${\mathcal U}$ of well-ordered nonmaximal prime ideals, to construct a discontinuous algebra norm  on ${\mathcal C}(K)$ for which all elements of ${\mathcal U}$ are $p$-closed.\\
Recent works by Hung Le Pham show that the situation is much more complicated in the general case and get close a complete answer to these questions. We will try to present here the state of the art, and describe how a "lifting problem," which can be formulated in ZFC, is the only remaining obstacle to a complete characterization of possible sets of $p$-closed nonmaximal prime ideals of  with respect to discontinouous algebra norms on ${\cal C}([0,1]).$ We will also discuss the open problem (in ZFC) of normability of a "big" algebra of power series described by Dales and Woodin in their monograph about hyper-real fields.


\bigskip
\item
\noindent {\bf Speaker}: David E.\ Evans (Cardiff University, UK)\\
\noindent {\bf Title}: The search for the exotic - subfactors and conformal field theories\\
\noindent {\bf Abstract}: Subfactor theory provides a framework for studying modular
invariant partition functions in conformal field theory,
and candidates for exotic modular tensor categories and almost
Calabi-Yau algebras.  I will describe some recent work which is also
motivated by links with twisted equivariant K-theory through the
K-theoretic realisation of Freed-Hopkins-Teleman of the Verlinde
algebra of primary fields.

This is joint work with Terry Gannon and  Mathew Pugh.


\bigskip
\item
\noindent {\bf Speaker}: Luis Ant\^onio Fernandes de Oliveira (UNESP - Ilha Solteira, Brazil)\\
\noindent {\bf Title}: Dushnik Integrals on C*-algebra of Regulated Functions $ G([a,b],X)$\\
\noindent {\bf Abstract}: In this paper we consider the Dushnik integral for regulated functions and we construct some examples of linear integral functionals on the C*-algebra
$G([a,b],{\cal A})$, where  ${\cal A} = C([a,b],\mathbb{R})$.


\bigskip
\item
\noindent {\bf Speaker}: Sanjiv Kumar Gupta (Sultan Qaboos University, Oman)\\
\noindent {\bf Title}: Asymmetry of Multipliers on Lie Groups\\
\noindent {\bf Abstract}: De Leeuw's multiplier theorem relates the multiplier on the circle group T and the real line R in a spectacular way. This result has been generalised in many ways in the context of non-commutative harmonic analysis, most notably by Coifman and Weiss. Let G be a real rank one semi--simple Lie group and G=KAN be its Iwasawa decomposition and M be the centraliser of A in K. An analogue of De Leeuw's theorem was proved by Rice, Dooley and Gaudry for the pair (K/M,N) for G=SO(p,1). But the transference of multipliers from N to K/M part was not the exact converse of the transference from K/M to N. In De Leeuw' s original theorem, transference from R to T and from T to R are exact converse to each other. Ricci and Rubin proved the transference from K/M to N for G=SU(2,1) but N to K/M case remained open. In this talk, I will present an exact analogue of De Leeuw's theorem for G=SU(p,1). Our work resolves a conjecture of C. Herz. This is joint work with A. Dooley and F. Ricci.



\bigskip
\item
\noindent {\bf Speaker}:  Haykel Gaaya (Unversit\'e Claude Bernard Lyon I, France)\\
\noindent {\bf Title}: On the higher rank numerical range of the shift operator\\
\noindent {\bf Abstract}: For any n-by-n complex matrix T and any $1\leqslant k\leqslant n$, let
$\Lambda_{k}(T)$ the set of all $\lambda\in \C$ such that $PTP=\lambda P$ for some rank-k orthogonal projection $P$ be its higher rank-k numerical range.
It is shown that if $\bbS$ is the n-dimensional shift on ${\C}^{n}$ then its rank-k numerical range is the circular disc centred in zero and with radius $\cos\dfrac{k\pi}{n+1}$ if $1<k\leqslant\left[\frac{n+1}{2} \right]$ and the empty set if $\left[\frac{n+1}{2} \right]<k\leqslant n$, where $\left[x \right] $ denote the integer part of $x$.
This extends and rafines previous results of U.\ Haagerup, P. de la Harpe \cite{Haagerup} on the classical numerical range of the n-dimensional shift on${\C}^{n}$. An interesting result for higher rank-$k$ numerical range of nilpotent operator is
also established.

\bigskip
\item
\noindent {\bf Speaker}: Messaoudene Hadia (University of Tebessa, Algeria) \\
\noindent {\bf Title}: The class of Jo\^el Anderson\\
\noindent {\bf Abstract}: The main objective of this work is to give more
informations about the class
of operators of Joel Anderson, noted by $\mathcal{JA}$($\mathcal{H}$); which
is the class of operators defined on the algebra of bounded linear operators
on a complex and infinite separable Hilbert space, for which the distance of
the identity operator and the derivation ranges is minimal, where the
derivation range of the operator A is defined by:
%\QTP{Body Math}
$$\delta _{A}:\mathcal{L(H)}\rightarrow \mathcal{L(H)}$$
%\QTP{Body Math}
$$X\mapsto AX-XA;\ A\ \in \mathcal{L(H)}.$$
%\QTP{Body Math}
Also to prove that the class $\mathcal{JA}(\mathcal{H})$ has no algebraic
structure and to give a necessary and sufficient condition for a bounded
linear operator $A$ to be in $\mathcal{JA}(\mathcal{H})$ and to obtain some
results concerning the form of operators in $\mathcal{JA}(\mathcal{H})$.


\bigskip
\item
\noindent {\bf Speaker}: Jan  Hamhalter and Ekaterina Turilova (Czech Technical
University in Prague, Czech Republic)\\
\noindent {\bf Title}:  Abelian and associative subalgebras determine the Jordan
structure\\
\noindent {\bf Abstract}: We present our recent results on the interplay between the Jordan
structure of $C^\ast$-algebras (resp. Jordan algebras) and the ordered
structure of their abelian $C^\ast$-subalgebras (resp. associative Jordan
subalgebras). Our prototype result is as follows: Let $Abel(A)$ be a system
of all unital abelian $C^\ast$-subalgebras of a unital $C^\ast$-algebra $A$
ordered by set inclusion. Then any order isomorphism $\varphi: Abel(A)\to
Abel(B)$, $dim A\ge 5$,   is implemented by a unique partially linear
Jordan $\ast$-isomorphism $\psi: A\to B$ in the sense that $\varphi
(C)=\psi(C)$ for all $C\in Abel(A)$.
(By a partially linear  map we mean a map linear when restricted to abelian
subalgebras.)   A similar  result holds for unital JB algebras and the
corresponding
structure of their unital associative JB-subalgebras. One of the
consequences
of our  analysis  says that poset of abelian unital $C^\ast$-subalgebras
(resp. associative unital JB subalgebras ) of a von Neumann algebra  (resp.
JBW algebra) without Type $I_2$ direct summand determines the Jordan
structure completely. The results above do not hold in nonunital case.
However, we show that  Jordan structure can be recovered from order
structure of associative (or abelian) subalgebras
endowed with an additional  natural orthogonality relation. We study also
the question of what additional structure on $Abel(A)$ makes it complete
$C^\ast$-invariant. The relation of our work to mathematical foundations of
quantum theory (including topos approach) is discussed.   Surprising aspect
of investigation along  this line seems to be  the fact that discrete order
structure of commutative subalgebras
is sometimes enough to encode entirely  functional analytic Jordan
structure.

\begin{thebibliography}{9}
\bibitem{Hamhalter}  J. Hamhalter: Isomorphisms of ordered structures of
abelian $C^\ast$-subalgebras of $C^\ast$-algebras, Journal of Mathematical
Analysis and Applications,
383, (2011), 391-399.
\bibitem{Common} J.Hamhalter and E.Turilova: {\em Structure of associative
subalgebras of Jordan operator algebras}, to appear.
\end{thebibliography}


\bigskip
\item
\noindent {\bf Speaker}: Robin Harte (Trinity College Dublin),
Dragan Djordjevic and Sne\v zana
Zivkovi\'c-Zlatanovi\'c (University of Nis)\\
\noindent {\bf Title}: Spectrale permanence \\
\noindent {\bf Abstract}: Three kinds of generalized inverse bounce off
one another in the proof of a technical observation about
C* algebras.\\ See further details at:
\href{http://www.math.ist.utl.pt/~elharti/3rd/ruston.pdf}
{http://www.math.ist.utl.pt/$\sim$elharti/3rd/ruston.pdf}


\bigskip
\item
\noindent {\bf Speaker}: Alexander A.\  Katz (St.\ John's University, USA)\\
\noindent {\bf Title}: On the notion of JB-bornological algebra\\
\noindent {\bf Abstract}: We introduce JB-bornological algebras as
bornological inductive limits of JB-subalgebras. Among other basic
properties we establish that for each JB-bornological algebra there
exists a unique universal enveloping C*-bornological algebra.


%\bigskip
%\item
%\noindent {\bf Speaker}:  Yasuyuki Kawahigashi (University of Tokyo, Japan)\\
%\noindent {\bf Title}: Superconformal field theory and operator algebras\\
%\noindent {\bf Abstract}: We describe operator algebraic approach to chiral
%superconformal field theory.  Based on some analogy between
%classifical differential geometry and conformal field theory,
%we present new connections between subfactor theory and
%noncommutative geometry through pairing of the $K$-theory
%and entire cyclic cohomology.


%\bigskip
%\item
%\noindent {\bf Speaker}: David Kerr (Texas A \&M University, USA)\\
%\noindent {\bf Title}: \\
%\noindent {\bf Abstract}:

\bigskip
\item
\noindent {\bf Speaker}: Bartosz Kwasniewski (University of Bialystok, Poland)\\
\noindent {\bf Title}: Uniqueness property for C*-algebras given by relations with circular
symmetry\\
\noindent {\bf Abstract}: The universal  $C^*$-algebras
$C^*(\mathcal{G},\mathcal{R})$ generated by a set  of operators
$\mathcal{G}$ subject to  given relations $\mathcal{R}$ include  the most
important classical examples of $C^*$-algebras. We propose a method of
dealing with the following issue:

\begin{itemize}
\item[ ] (\emph{uniqueness problem}) Do there exist two  representations of
$(\mathcal{G},\mathcal{R})$ that generate non-isomorphic $C^*$-algebras?
\end{itemize}

The set  of relations $\mathcal{R}$ that defines  the classical algebras
usually possess a natural circular symmetry, that yields  a circle action
 $\gamma$ on $C^*(\mathcal{G},\mathcal{R})$ such that
$C^*(\mathcal{G},\mathcal{R})$ is generated by the fixed point algebra
$\mathcal{B}_0$ and the first spectral subspace $\mathcal{B}_1$ for
$\gamma$. The pair $(\mathcal{B}_0,\mathcal{B}_1)$ is naturally equipped
with a structure of a Hilbert bimodule and one can recover
$C^*(\mathcal{G},\mathcal{R})$ from $(\mathcal{B}_0,\mathcal{B}_1)$ by
means of the crossed product introduced in \cite{exel-inter}. Thus the
following scheme of investigation of $C^*(\mathcal{G},\mathcal{R})$ seems
to be inevitable:

\begin{center}  \setlength{\unitlength}{0.53mm}
\begin{picture}(170,20)(20,0) \put(-5,8){$ \xymatrix{
(\mathcal{G},\mathcal{R}, \{\gamma_\lambda\}_{\lambda \in S^1})\ar[rr] &  &
 (\mathcal{B}_0,\mathcal{B}_1)  \ar[rr]  & &
C^*(\mathcal{G},\mathcal{R})=C^*(\mathcal{B}_0,\mathcal{B}_1)}$}

 \put(-3,0){\tiny relations,   circle action}   \put(83,0){\tiny Hilbert
bimodule}   \put(165,0){ \tiny universal $C^*$-algebra}     \end{picture}
\end{center}

In our approach we treat $(\mathcal{B}_0,\mathcal{B}_1)$ as a
\emph{non-commutative reversible dynamical system} attached to
$(\mathcal{G},\mathcal{R})$ and we show that if this system  is
topologically free, then the pair   $(\mathcal{G},\mathcal{R})$  possess
 \emph{uniqueness property} (the answer to the uniqueness problem is
``no'').  When applied   to specific examples this theorem leads to
generalizations of isomorphism theorems for various crossed products, and
is shown to be equivalent to classical Cuntz-Krieger uniqueness theorem
\cite{CK}.  On the latter occasion an intriguing realization of
Cuntz-Krieger algebras as \emph{crossed products by interactions}
 \cite{exel-inter} is discovered.

The presentation is based on \cite{kwa}.

\begin{thebibliography}{99}
\bibitem[AEE98]{aee}
B. Abadie, S. Eilers, R. Exel, \emph{Morita equivalence for crossed
products by Hilbert $C^*$-bimodules},
Trans. Amer. Math. Soc.,
\textbf{ 350} (1998), No. 8,  3043-3054.  \bibitem[CK80]{CK} J. Cuntz, W.
Krieger, \emph{A class of $C^*$-algebras and topological Markov chains},
Invetiones Math. \textbf{56} (1980), 256-268.

\bibitem[Exe07]{exel-inter}
R. Exel, {\em Interactions} Funct. Analysis, 244 (2007), 26 - 62
\bibitem[Kwa]{kwa} B. K. Kwa\'sniewski \emph{Cuntz-Krieger uniqueness
theorem for crossed products by Hilbert bimodules}  preprint
arXiv:1010.0446
\end{thebibliography}


\bigskip
\item
\noindent {\bf Speaker}: Nuno Martins (IST lisbon, Portugal)\\
\noindent {\bf Title}: Representations of C*-algebras from interval maps\\
\noindent {\bf Abstract}: Given a family of interval maps, we construct partial isometries acting on
Hilbert spaces associated to the orbit of each point. Then we prove that
such partial isometries give rise to representations of certain C*-algebras.
We study the irreducibility of these representations. Finally, we state the
conditions to have unitarily equivalence between two such representations.

This talk is based on joint works with C. Correia Ramos, R. El Harti and P.
Pinto.


\bigskip
\item
\noindent {\bf Speaker}: Sidi Mohamed Bahri (Universit� Abdelhamid Ibn Badis Mostaganem, Algerie)\\
\noindent {\bf Title}: On the quasi-selfadjoint extensions of a Carleman operator\\
\noindent {\bf Abstract}: In the present work, using a formula describing all scalar spectral functions of a Carleman operator A of defect indices (1,1) in the Hilbert space
$L^2(X)$ that we obtained in a previous paper, we derive certain results
concerning the localization of the spectrum of quasi-selfadjoint extensions of
the operator A.

\bigskip
\item
\noindent {\bf Speaker}: Mostafa Mbekhta (University of  Lille I, France)\\
\noindent {\bf Title}: Survey on preserver problems and generalized invertibility\\
\noindent {\bf Abstract}: This survey is articulated around two major axis. The first one concerns
the Kaplansky problem; the history of the problem and several results are
presented. The second one concerns some new preserver problems (concern-
ing the generalized inverse, Fredholm or semi-Fredholm operators...). The
common point of these results is that they are interesting only in the infinite
dimensional situation.

References

$[1]$\ B. Aupetit, Sur les transformations qui conservent le spectre, Banach
Algebra'97 (Walter de Gruyter, Berlin), (1998), 55-78

$[2]$\ B. Aupetit, Spectrum-preserving linear mappings between Banach
algebras or Jordan-Banach algebras, J. London Math. Soc. 62 (2000), 917-924.

$[3]$\ N. Boudi and M. Mbekhta Additive maps preserving strongly generalized
inverses J. Operator Theory 64 (2010), 117-130.

$[4]$\ M. Mbekhta, L. Rodman, and P. Semrl, Linear maps preserving generalized
invertibility, Int. Equ. Op. Th. 55 (2006), 93-109.

$[5]$\ M. Mbekhta, Linear maps preserving a set of Fredholm operators, Proc.
Amer. Math. Soc. 135 (2007) 3613-3619.

$[6]$\ M. Mbekhta and P. Semrl, Linear maps preserving semi-Fredholm
operators and generalized invertibility, Linear and Multilinear Algebra, 57
(2009), 55-65.

$[7]$\ A.R. Sourour, Invertibility preserving linear maps on $L(X)$, Trans. Amer.
Math. Soc. 348 (1996), 13-30.




\bigskip
\item
\noindent {\bf Speaker}: Sergio Mendes (Lisbon University Institute, Portugal)\\
\noindent {\bf Title}: A note on the reduced Iwahori-Hecke $C^*$-algebra of $GL(n)$\\
\noindent {\bf Abstract}: According to the Baum-Connes conjecture for $G=GL(n)$, there is a canonical
isomorphism
$$\mu:K_*^G(\underline{E}G)\rightarrow K_*C_r^*G$$
where $\underline{E}G$ is a universal example for the action of $G$. Quite
specific, $\underline{E}G$ is the affine Bruhat-Tits building
for G, also denoted $\beta G$. Let $C_r^*(G//I)$ denote the reduced
Iwahori-Hecke $C^*$-algebra of $GL(n)$ and let $\Sigma$ be a single
apartment in $\beta G$. Then, $\Sigma=\underline{E}W$ is a model for the
universal example $\underline{E}W$ of the the affine Weyl group $W$ of $G$.
Localized to the apartment $\Sigma$, the  Baum-Connes conjecture modulo
torsion is an isomorphism

$$K_j(C_r^*(G//I)\otimes_{\mathbb{Z}}\mathbb{C}\cong
K_j^W(\Sigma)\otimes_{\mathbb{Z}}\mathbb{C}.$$

Let $E/F$ be a finite Galois extension of local nonarchimedean fields. Base
change lifts a representation of $GL(n,F)$ to a representation of
$GL(n,E)$. This creates a map from the tempered dual of $GL(n,F)$ to the
tempered dual of $GL(n,E)$. We use the Baum-Connes conjecture to relate
functoriality of buildings with base change. We illustrate this relation
with the reduced Iwahori-Hecke $C^*$-algebra of $GL(n,E)$ and $GL(n,F)$.


\bigskip
\item
\noindent {\bf Speaker}:  Abdelaziz Mennouni (University of Bordj Bou-Arreridj, Algeria)\\
\noindent {\bf Title}: Closed Form Expression for the Solution of Some Singular Integral Equations\\
\noindent {\bf Abstract}: This paper investigates the exact solution of some singular integral equations of the first kind.
We present a new technique in such a manner that Adomian's decomposition method can be applied.
We obtain a closed form expression for the solution of this class. In the end, some numerical examples with closed-form solutions illustrate the theoretical results.


%\bigskip
%\item
%\noindent {\bf Speaker}: Mohammad Sal Moslehian (Ferdowsi Univ. of Mashhad, Iran)\\
%\noindent {\bf Title}: \\
%\noindent {\bf Abstract}:


\bigskip
\item
\noindent {\bf Speaker}: Zouhair Mouayn (University Moulay Slimane, Morocco)\\
\noindent {\bf Title}: Coherent states for Landau levels on two-dimensional surfaces and
associated photon counting probability distributions\\
\noindent {\bf Abstract}: Generalized
coherent states attached to Landau levels on two-dimensional surfaces are
constructed. The associated
counting probability distributions are defined and their main statistical
parameters are
obtained. As application, we discuss the classicality/nonclassicality of
the constructed states
 with respect to the location of their labeling points.


\bigskip
\item
\noindent {\bf Speaker}: Nobuaki Obata (Tohoku University, Japan)\\
\noindent {\bf Title}: Spectral analysis of product graphs -- A quantum probabilistic view point\\
\noindent {\bf Abstract}:
In recent years, quantum probability has been applied to spectral
analysis of graphs,
in particular, to the study of spectral properties of the adjacency
matrices of
(large, growing, or random) graphs. In this talk we focus on the product
structures of graphs (Cartesian, comb, star, free, etc). It is noted
that product
structures are related to various concepts of independence in quantum
probability theory.
From this aspect the spectral distribution is obtained from suitable
convolution products of
probability measures. We will review basic results and report some
recent achievements
on the Manhattan product of digraphs for future direction.\\
$[1]$ A.\ Hora and N. Obata: Quantum Probability and Spectral Analysis of Graphs Springer, 2007.\\
$[2]$ N.\ Obata: Lecture Notes (Tokyo, Sendai, Wroclaw, Cheongju, etc)\\
available at http://www.math.is.tohoku.ac.jp/~obata/


\bigskip
\item
\noindent {\bf Speaker}: Vladimir Peller (Michigan State University, USA)\\
\noindent {\bf Title}: Operator moduli of continuity\\
\noindent {\bf Abstract}: We study properties of operator moduli of continuity. For a continuous
function $f$ on a closed subset ${\frak F}$ of the real line the operator
modulus of continuity $\Omega_f$ is defined by
$$\Omega_f(\delta)=\sup\|f(A)-f(B)\|,\quad \delta>0,$$
where the supremum is taken over all self-adjoint operators $A$ and $B$
with spectra in ${\frak F}$ such that $\|A-B\|<\delta$.\\
I am going to speak about upper and lower estimates for the operator moduli
of continuity. The talked is based on joint work with A.B.\ Aleksandrov.


\bigskip
\item
\noindent {\bf Speaker}: Paulo R.\ Pinto (IST Lisbon, Portugal)\\
\noindent {\bf Title}: On the profinite completion of group-C*-algebras\\
\noindent {\bf Abstract}:  We investigate when a C$^\ast$-algebra $A$ can be given
different structures of pro-C$^\ast$-algebras, leading us to define
the profinite completion of a C*-algebra (which is a pro-C*-algebra).\\
As an analog of the diagonal group
morphism from a group into its profinite completion,
we construct a natural homomorphism
from the group C*-algebra of a locally
compact group to the pro-C*-algebra
of the profinite completion of the group.
We prove that this homomorphism is indeed injective
for amenable residually finite discrete groups.
The talk is based on a joint work with R.\ El Harti
and N.C.\ Phillips.


%\bigskip
%\item
%\noindent {\bf Speaker}: Alexei Pirkovskii (National Research University, Russia)\\
%\noindent {\bf Title}: \\
%\noindent {\bf Abstract}:


\bigskip
\item
\noindent {\bf Speaker}: Jean Renault (University d'Orl\'eans, France)\\
\noindent {\bf Title}: Groupoid cocycles and derivations\\
\noindent {\bf Abstract}: There are a number of results which say that, under suitable hypotheses, cocycles which are bounded are necessarily coboundaries and that bounded derivations are inner. I shall review these results and give them some natural extensions in the framework of  locally compact groupoids and Hilbert C*-modules. I will give examples and applications.


\bigskip
\item
\noindent {\bf Speaker}: Mohammed A.\ Salim (United Arab Emirates University)\\
\noindent {\bf Title}: About Zassenhaus and Conjecture for Torsion Units in Integral Group Rings\\
\noindent {\bf Abstract}: Using the Luthur-Passi method and results of Hertweck, we
consider the famous Zassenhaus Conjecture for the normalized unit group of
the integral group ring of the symmetric groups $S_{n},n\leq 10$. As a
consequence, we achieve the solution of the Kimmerle's conjecture about
prime graphs for the group of units of these groups.

\bigskip
\item
\noindent {\bf Speaker}: Markus Seidel (Chemnitz University of Technology, Germany)\\
\noindent {\bf Title}: Approximate projections, $\mathcal{P}$-strong convergence and the finite sections of quasi-diagonal operators\\
\noindent {\bf Abstract}: The notions of compact operators, Fredholm operators and strong convergence as well as
the interactions between them have played a crucial role and have been intensively
exploited in the theory of projection methods for bounded linear operators.
More precisely, for a given equation $Ax=b$ with the unknown $x$, one chooses a
strongly converging sequence of compact projections $\mathcal{P}=(P_n)$ and one
studies the sequence of equations $P_nAP_nx_n=P_nb$, $n\in \mathbb{N}$, in order
to find approximate solutions for the initial problem.\\
We now turn the table, in a sense, and take a sequence $\mathcal{P}=(P_n)$, being
a so-called approximate projection, as a starting point for the definition
of the substitutes $\mathcal{P}$-compactness, $\mathcal{P}$-Fredholmness and
$\mathcal{P}$-strong convergence. This adapted framework enables us to develop a
theory that mimics the classical one, provides very similar results on the
applicability of the projection method, the stability, and on the convergence of norms,
condition numbers or pseudospectra, but extends them to much more general
settings.\\
We demonstrate the approach for the finite section method applied to quasi-diagonal
operators acting on certain Banach spaces, e.g. $l^p(\mathbb{Z})$ or $L^p(\mathbb{R})$
with $1\leq p \leq \infty$.

%\bigskip
%\noindent {\bf Speaker}: Ilya Spitkovsky (College of William \& Mary of Williamsburg, USA)\\
%\noindent {\bf Title}: \\
%\noindent {\bf Abstract}:

\bigskip
\item
\noindent {\bf Speaker}: Janusz Wysocza\~nski (University of Wrocaw, Poland)\\
\noindent {\bf Title}: Ortjogonal polynomials rel�ated to anyon statistics\\
\noindent {\bf Abstract}: Let $T$ be a locally compact Polish space (i.e. separable,
completely metrizable topological space), with a non-atomic Radon
measure $\sigma$. Let $D\subset T\times T$ be the diagonal:
\[
D := \{(t, t) \in T^2 | t \in T\}
\] Let also $A\subset T\times T$ be symmetric subset, i.e. if $(s,t)\in
A$ then $(t,s)\in A$, containing the diagonal $D\subset A$. We
consider a hermitian kernel (on the complement of $A$):
\[
Q: (T\times T \setminus A) \rightarrow S^1:=\{z\in \mathbb{C}: |z|=1
\}, \quad Q(s,t)= \overline{Q(t,s)}.
\]
The basic example is the anyonic case: for $T=\mathbb{R}$ or
$T=\mathbb{R}^+$ and $A=D$ and fixed $|q|=1$ we put
\[
Q(s, t):= \left\{
\begin{array}{ccc}
q&\mbox{if}&s<t\\
\overline{q}&\mbox{if}&t<s
\end{array}
\right.
\]
This allows us to define the $Q$-deformed (i.e. $Q$-symmetric) Fock
space (for $L^2(T, \sigma)$) and, for a given $h\in L^2(T, \sigma)$,
the related $Q$-creation $a^{\dagger}(h)$, $Q$-annihilation $a(h)$
and $Q$-neutral $a^0(h)$ operators. Moreover, we give meaning to the
$Q$-creation, $Q$-annihilation and $Q$-neutral operators at points:
\[
a^{\dagger}(\delta_t):= \prd_t, \quad a(\delta_t):=\pr_t, \quad
a^0(\delta_t):= \prd_t\pr_t,
\]
and for these we obtain some deformed commutation relations:
\begin{eqnarray*}
\pr_s\prd_t &=& \delta(s, t)+Q(s, t)\prd_t\pr_s \\
\pr_s\pr_t &=& Q(t, s)\pr_t\pr_s \\
\prd_s\prd_t &=& Q(t, s)\prd_t\prd_s \label{pr++}
\end{eqnarray*}
For $\lambda > 0$ we put
\[
\wt := \prd_t+\lambda \prd_t\pr_t + \pr_t.
\]
This defines the generalized $Q$-Gaussian process $(\lambda = 0)$
and $Q$-Poisson (centered) process $(\lambda = 1)$. Then we study
the related $Q$-Hermite $(\lambda = 0)$ and $Q$-Charlier $(\lambda =
0)$  orthogonal polynomials. We obtain some recurrence relations for
them and also study the associated Wick ordering. The description we
obtain uses marked partitions.

The talk is based on the paper:\\
{Bo{\.z}ejko, M., Lytvynov, E. Wysocza{\'n}ski, J.} {\em
"Non-commutative L\'{e}vy processes for generalized (particularly
anyon) statistics "} (2011), {to appear}.



















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\end{enumerate}


\end{document}
