RECASTING THE ELLIOTT CONJECTURE

Let A be a simple, unital, finite, and exact C*-algebra which absorbs the Jiang-Su algebra Z tensorially. We prove that the Cuntz semigroup of A admits a complete order embedding into an ordered semigroup which is obtained from the Elliott invariant in a functorial manner. We conjecture that this embedding is an isomor phism, and prove the conjecture in several cases. In these same cases - Z-stable algebras all - we prove that the Elliott conjecture in its strongest form is equivalent to a conjecture which appears much weaker. Outside the class of Z-stable C*-algebras, this weaker conjecture has no known counterexamples, and it is plausible that none exist. Thus, we reconcile the still intact principle of Elliott's classification conjecture -that K-theoretic invariants will classify separable and nuclear C*-algebras- with the recent appearance of counterexamples to its strongest concrete form.

Stable rank of leavitt path algebra

We characterize the values of the stable rank for Leavitt path algebras, by giving concrete criteria in terms of properties of the underlying graph.

Model structures on the category of small double categories

In this paper we obtain several model structures on DblCat, the category of small double categories. Our model structures have three sources. We first transfer across a categorification-nerve adjunction. Secondly, we view double categories as internal categories in Cat and take as our weak equivalences various internal equivalences defined via Grothendieck topologies. Thirdly, DblCat inherits a model structure as a category of algebras over a 2-monad. Some of these model structures coincide and the different points of view give us further results about cofibrant replacements and cofi brant objects. As part of this program we give explicit descriptions and discuss properties of free double categories, quotient double categories, colimits of double categories, and several nerves and categorifications.

Quantum symmetries for exceptional SU(4) modular invariants associated with conformal embeddings

Three exceptional modular invariants of SU(4) exist at levels 4, 6 and 8. They can be obtained from appropriate conformal embeddings and the corresponding graphs have self-fusion. From these embeddings, or from their associated modular invariants, we determine the algebras of quantum symmetries, obtain their generators,and, as a by-product, recover the known graphs E4, E6 and E8 describing exceptional quantum subgroups of type SU(4). We also obtain characteristic numbers (quantum cardinalities, dimensions) for each of them and for their associated quantum groupoïds.

Aplicacions contínues entre espais classificadors de grups p-locals finits

Projecte de recerca elaborat a partir d’una estada a la Universitat d'Aberdeen, Irlanda, entre abril i maig del 2007. Un dels objectius de la topologia algebraica és la de classificar espais topològics i aplicacions continues mitjançant estructures algebraiques associades a ells. És a dir, mitjançant diferents maneres d'associar un objecte algebraic a un espai, es pretén reflectir el màxim de la seva estructura topològica. D'altra banda, donat un grup G, se li pot associar un espai topològic BG anomenat l'espai classificador del grup que és l'espai que classifica els G-fibrats vectorials. El programa d'estudiar el tipus d'homotopia d'espais i aplicacions contínues ha donat molts fruits quan els espais que s'estudien són espais classificadors (en particular, grups finits i grups de Lie). En particular, a causa del fet que moltes propietats algebraiques del grup queden reflectides en l'espai classificador, aquest tipus d'espais juguen un paper molt important en la interelació entre l'àlgebra i la topologia. Per exemple, els treballs de Dwyer, Zabrodsky i Mislin identifiquen les aplicacions contínues entre espais classificadors d'un p-grup i un grup qualsevol amb els morfismes entre grups llevat conjugació. L’objectiu d’aquest projecte és el de descriure les aplicacions contínues entre p-completats d’espais classificadors a partir d’informació algebraica referent a l’estructura de p-subgrups de cadascun d’ells.

Narrating urban entrepreneurship: a matter of imagineering?

The battle between cities with regard to their creative possibilities has evolved into a process of multiplying ever-new images and variegated stories of urban attractiveness and success. Engineering “cool” images and “hot” stories about one’s city is now a central endeavor in the narratives of urban policy-making that center more and more on the idea of the entrepreneurial city. The making of an entrepreneurial image is enacted through various narrative genres that lie somewhere between place making and place marketing, between branding and boosting, between restoration and revanchism, between iconic architecture and mega-spectacle. This “imagineering” is not only part of the way cities try to (re)present themselves as entrepreneurial to various audiences through a real “image inflation” (Zukin, 2008, p. xii) but is 1 Forthcoming in: B. Lange,.A. Kalandides, B. Stoeber, I. Wellmann (Hrsg.) (2009): Governance der Kreativwirtschaft. Diagnosen und Handlungsoptionen. Transcript-Verlag, Bielefeld. 2 also inscribed in the various ways urban creativity and entrepreneurship can be studied, researched and imagined. In this chapter we aim to differentiate the political narratives of the entrepreneurial city as we emphasize the need to understand the politics of narration and make a plea for critical reflexivity in our forms of researching and theorizing. We will thus try to investigate how the politics of narration is intertwined with the narration of political concepts and will argue that the narrating of urban entrepreneurship can raise very different images and discourses of city life beyond those that are currently engineered. We will distinguish between a grand narrative, a counter-narrative, and an assemblage of more ambivalent little narratives, which we call prosaic narration. While the distinction between these three types might be seen as a bit too simple and “straight”, we believe that by juxtaposing these different forms of narration and alternating between them, we can help problematize the engineering of the city as entrepreneurial and imagine alternative views both of city life and of what is understood as its creativity.

A model structure for coloured operads in symmetric spectra

We describe a model structure for coloured operads with values in the category of symmetric spectra (with the positive model structure), in which fibrations and weak equivalences are defined at the level of the underlying collections. This allows us to treat R-module spectra (where R is a cofibrant ring spectrum) as algebras over a cofibrant spectrum-valued operad with R as its first term. Using this model structure, we give sufficient conditions for homotopical localizations in the category of symmetric spectra to preserve module structures.

Equivariant semiprojectivity

We define equivariant semiprojectivity for C* -algebras equipped with actions of compact groups. We prove that the following examples are equivariantly semiprojective: A. Arbitrary finite dimensional C*-algebras with arbitrary actions of compact groups. - B. The Cuntz algebras Od and extended Cuntz algebras Ed, for finite d, with quasifree actions of compact groups. - C. The Cuntz algebra O∞ with any quasifree action of a finite group. For actions of finite groups, we prove that equivariant semiprojectivity is equiv- alent to a form of equivariant stability of generators and relations. We also prove that if G is finite, then C*(G) is graded semiprojective.

International regimes as knowledge syndicates? Energy and trends of global governance

El poder de l'Estat i la sobirania tradicional s'està deteriorant de manera constant, sobretot en termes de la provisió de certs béns públics fonamentals. Els Estats, en particular, són incapaços de manejar el coneixement i la informació que és essencial per mantenir la competitivitat i la sostenibilitat en una economia interdependent. Estructures fiables de la governança mundial i la cooperació internacional estan lluny de ser establertes. Energia com a problema a les agendes p dels governs, les empreses privades i la societat civil és un exemple manifest d'aquesta dinàmica.. L'actual sistema de governança mundial d'energia implica accions polítiques disperses per actors divers. L'Agència Internacional de l'Energia té un paper destacat, però està debilitat per la seva composició limitada i basada en el coneixement- epistèmic en lloc del material o executiu. Aquest treball sosté que ni la mida ni nombre de membres disponibles estan dificultant la governabilitat mundial d'energia. Més aviat, l'energia és una sèrie de béns públics que es troben als llimbs, on els estats no poden pagar la seva disposició, així com els diversos interessos impedir l'establiment d'una autoritat internacional. Després de la introducció de la teoria del règim internacional i el concepte de coneixement basats en les comunitats epistèmiques, l'article revisa l'estat actual de la governabilitat de l'energia mundia. A continuació es presenta una comparació d'aquesta estructura amb els règims de govern nacional i regional, d'una banda, i amb règims globals ambientals i de salut, de l'altra

China’s Strategy in North Africa: New economic challenges for the Mediterranean region

El WP té com a objectiu examinar per què els països del nord d'Àfrica estan augmentant les seves importacions de Xina i per què la Xina està augmentant les seves inversions estrangeres directes a la zona. la avantatges per als països del nord d'Àfrica es troben en els actuals acords de lliure comerç, el absència de barreres aranzelàries i la seva ubicació geogràfica summament beneficiosa com Hub de la Mediterrània. El paper de la Unió per la Mediterrània és clau per identificar aspectes de la política regional, tenint en compte la participació xinesa a la zona. com conseqüència, concloem que els actors polítics han de trobar un equilibri entre sostenible desenvolupament i els interessos econòmics de la regió.

Variétés CR polarisées et G-polarisées, partie I

Polarized and G-polarized CR manifolds are smooth manifolds endowed with a double structure: a real foliation &em&F&/em& (given by the action of a Lie group G in the G-polarized case) and a transverse CR distribution. Polarized means that (E,J) is roughly speaking invariant by&em&F&/em&. Both structures are therefore linked up. The interplay between them gives to polarized CR-manifolds a very rich geometry. In this paper, we study the properties of polarized and G-polarized manifolds, putting special emphasis on their deformations.

Do women in female-dominated occupations exit the labour market more? Evidence from Italy, Spain, Denmark and the UK

Literature on sex occupational segregation has typically focused on the micro and macro determinants of it, on mobility patterns over the life course, on implications of segregation and mobility for gender inequalities. Rarely the link between sex-type occupations and women’s risk of labour market interruptions over family formation has been explored. In this piece of work we shall analyse whether women who are working in the female-dominated, male-dominated or integrated occupations have more or less chances to remain attached to the labour market, controlling for qualifications, class, sector and contract positions. By drawing from ECHP, and comparing Italy, Spain, Denmark and the UK, we shall in particular see whether such connection varies across countries with different institutional and cultural configurations.We find that, ceteris paribus, only in the UK the sex-composition of an occupation matters: women in female occupations are more likely to move to inactivity than women in mixed or male occupations. In the other countries considered the main cleavages lie elsewhere. In Italy what matters most is the sector of employment (public vs. private). In Spain the sector is relevant too, but also social class and the type of contract held (permanent vs. temporary). In Denmark women’s transitions to inactivity are largely independent of human capital and job characteristics.

Federalism and democracy. The case of minority nations: a federalist deficit

In this chapter, after pointing out the different logics that lie behind the familiar ideas of democracy and federalism, I have dealt with the case of plurinational federal democracies. Having put forward a double criterion of an empirical nature with which to differentiate between the existence of minority nations within plurinational democracies (section 2), I suggest three theoretical criteria for the political accommodation of these democracies. In the following section, I show the agonistic nature of the normative discussion of the political accommodation of this kind of democracies, which bring monist and pluralist versions of the demos of the polity into conflict (section 3.1), as well as a number of conclusions which are the result of a comparative study of 19 federal and regional democracies using four analytical axes: the uninational/plurinational axis; the unitarianism-federalism axis; the centralisation-decentralisation axis; and the symmetry-asymmetry axis (section 3.2). This analysis reveals shortcomings in the constitutional recognition of national pluralism in federal and regional cases with a large number of federated units/regions with political autonomy; a lower degree of constitutional federalism and a greater asymmetry in the federated entities or regions of plurinational democracies. It also reveals difficulties to establish clear formulas in these democracies in order to encourage a “federalism of trust” based on the participation and protection of national minorities in the shared government of plurinational federations/regional states. Actually, there is a federal deficit in this kind polities according to normative liberal-democratic patterns and to what comparative analysis show. Finally, this chapter advocates the need for a greater normative and institutional refinement in plurinational federal democracies. In order to achieve this, it is necessary to introduce a deeper form of “ethical” pluralism -which displays normative agonistic trends, as well as a more “confederal/asymmetrical” perspective, congruent with the national pluralism of these kind of polities.

Experimental design on the simplex

Optimum experimental designs depend on the design criterion, the model andthe design region. The talk will consider the design of experiments for regressionmodels in which there is a single response with the explanatory variables lying ina simplex. One example is experiments on various compositions of glass such asthose considered by Martin, Bursnall, and Stillman (2001).Because of the highly symmetric nature of the simplex, the class of models thatare of interest, typically Scheff´e polynomials (Scheff´e 1958) are rather differentfrom those of standard regression analysis. The optimum designs are also ratherdifferent, inheriting a high degree of symmetry from the models.In the talk I will hope to discuss a variety of modes for such experiments. ThenI will discuss constrained mixture experiments, when not all the simplex is availablefor experimentation. Other important aspects include mixture experimentswith extra non-mixture factors and the blocking of mixture experiments.Much of the material is in Chapter 16 of Atkinson, Donev, and Tobias (2007).If time and my research allows, I would hope to finish with a few comments ondesign when the responses, rather than the explanatory variables, lie in a simplex.ReferencesAtkinson, A. C., A. N. Donev, and R. D. Tobias (2007). Optimum ExperimentalDesigns, with SAS. Oxford: Oxford University Press.Martin, R. J., M. C. Bursnall, and E. C. Stillman (2001). Further results onoptimal and efficient designs for constrained mixture experiments. In A. C.Atkinson, B. Bogacka, and A. Zhigljavsky (Eds.), Optimal Design 2000,pp. 225–239. Dordrecht: Kluwer.Scheff´e, H. (1958). Experiments with mixtures. Journal of the Royal StatisticalSociety, Ser. B 20, 344–360.1

A multilevel analysis on the determinants of regional health care expenditure. A note

We apply a multilevel hierarchical model to explore whether anaggregation fallacy exists in estimating the income elasticity of healthexpenditure by ignoring the regional composition of national healthexpenditure figures. We use data for 110 regions in eight OECD countriesin 1997: Australia, Canada, France, Germany, Italy, Spain, Sweden andUnited Kingdom. In doing this we have tried to identify two sources ofrandom variation: within countries and between-countries. Our resultsshow that: 1- Variability between countries amounts to (SD) 0.5433, andjust 13% of that can be attributed to income elasticity and the remaining87% to autonomous health expenditure; 2- Within countries, variabilityamounts to (SD) 1.0249; and 3- The intra-class correlation is 0.5300. Weconclude that we have to take into account the degree of fiscaldecentralisation within countries in estimating income elasticity ofhealth expenditure. Two reasons lie behind this: a) where there isdecentralisation to the regions, policies aimed at emulating diversitytend to increase national health care expenditure; and b) without fiscaldecentralisation, central monitoring of finance tends to reduce regionaldiversity and therefore decrease national health expenditure.