La proyección y el nivel de competencia del profesor tutor. Acciones metodológicas para su potenciación

In the investigation, elements related to the projection and competence of the tutor professor are provided, supported by the diagnosis made in the process of investigative work practice in the Faculty of Physical Culture of Guantanamo, which reveals limitations in advising students, from Hence, methodological actions are proposed for its empowerment. Scientific methods were used that allowed to reveal and explain the current state of the problem and the collection of information based on the achievement of the objectives. With the application of methodological actions, it was possible to improve the level of competence of the adviser professors.En la investigación se brindan elementos relativos a la proyección y competencia del profesor tutor, sustentado a partir del diagnóstico realizado en el proceso de la práctica laboral investigativa en la facultad de Cultura Física de Guantánamo, que revela limitaciones en la asesoría de los estudiantes, de ahí que se proponen acciones metodológicas para su potenciación. Se emplearon métodos científicos que permitieron revelar y explicar el estado actual del problema y la recogida de información en función del logro de los objetivos. Con la aplicación de las acciones metodológicas se logró mejorar el nivel de competencia de los profesores tutores

Rigidity results for Bernoulli actions and their von Neumann algebras (after Sorin Popa)

We survey Sorin Popa's recent work on Bernoulli actions. The paper was written on the occasion of the Bourbaki seminar. Using very original methods from operator algebras, Sorin Popa has shown that the orbit structure of the Bernoulli action of a property (T) group, completely remembers the group and the action. This information is even essentially contained in the crossed product von Neumann algebra, yielding the first von Neumann strong rigidity theorem in the literature. The same methods allow Popa to obtain II_1 factors with prescribed countable fundamental group.Comment: Minor correction

W*-superrigidity for Bernoulli actions of property (T) groups

We consider group measure space II$_1$ factors $M=L^{\infty}(X)\rtimes\Gamma$ arising from Bernoulli actions of ICC property (T) groups $\Gamma$ (more generally, of groups $\Gamma$ containing an infinite normal subgroup with relative property (T)) and prove a rigidity result for *--homomorphisms $\theta:M\to M\bar{\otimes}M$. We deduce that the action $\Gamma\curvearrowright X$ is W$^*$--superrigid. This means that if $\Lambda\curvearrowright Y$ is {\bf any other} free, ergodic, measure preserving action such that the factors $M=L^{\infty}(X)\rtimes\Gamma$ and $L^{\infty}(Y)\rtimes\Lambda$ are isomorphic, then the actions $\Gamma\curvearrowright X$ and $\Lambda\curvearrowright Y$ must be conjugate. Moreover, we show that if $p\in M\setminus\{1\}$ is a projection, then $pMp$ does not admit a group measure space decomposition nor a group von Neumann algebra decomposition (the latter under the additional assumption that $\Gamma$ is torsion free). We also prove a rigidity result for *--homomorphisms $\theta:M\to M$, this time for $\Gamma$ in a larger class of groups than above, now including products of non--amenable groups. For certain groups $\Gamma$, e.g. $\Gamma=\Bbb F_2\times\Bbb F_2$, we deduce that $M$ does not embed in $pMp$, for any projection $p\in M\setminus\{1\}$, and obtain a description of the endomorphism semigroup of $M$.Comment: The revised version includes a new application: examples of II_1 factors which are not isomorphic to twisted group von Neumann algebra

Consensus using Asynchronous Failure Detectors

The FLP result shows that crash-tolerant consensus is impossible to solve in asynchronous systems, and several solutions have been proposed for crash-tolerant consensus under alternative (stronger) models. One popular approach is to augment the asynchronous system with appropriate failure detectors, which provide (potentially unreliable) information about process crashes in the system, to circumvent the FLP impossibility. In this paper, we demonstrate the exact mechanism by which (sufficiently powerful) asynchronous failure detectors enable solving crash-tolerant consensus. Our approach, which borrows arguments from the FLP impossibility proof and the famous result from CHT, which shows that $\Omega$ is a weakest failure detector to solve consensus, also yields a natural proof to $\Omega$ as a weakest asynchronous failure detector to solve consensus. The use of I/O automata theory in our approach enables us to model execution in a more detailed fashion than CHT and also addresses the latent assumptions and assertions in the original result in CHT

Explicit computations of all finite index bimodules for a family of II_1 factors

We study II_1 factors M and N associated with good generalized Bernoulli actions of groups having an infinite almost normal subgroup with the relative property (T). We prove the following rigidity result: every finite index M-N-bimodule (in particular, every isomorphism between M and N) is described by a commensurability of the groups involved and a commensurability of their actions. The fusion algebra of finite index M-M-bimodules is identified with an extended Hecke fusion algebra, providing the first explicit computations of the fusion algebra of a II_1 factor. We obtain in particular explicit examples of II_1 factors with trivial fusion algebra, i.e. only having trivial finite index subfactors.Comment: Minor modifications, final versio

On Sofic Actions and Equivalence Relations

The notion of sofic equivalence relation was introduced by Gabor Elek and Gabor Lippner. Their technics employ some graph theory. Here we define this notion in a more operator algebraic context, starting from Connes' embedding problem, and prove the equivalence of this two definitions. We introduce a notion of sofic action for an arbitrary group and prove that amalgamated product of sofic actions over amenable groups is again sofic. We also prove that amalgamated product of sofic groups over an amenable subgroup is again sofic.Comment: Improved version after remark

Rigid supersymmetry with boundaries

We construct rigidly supersymmetric bulk-plus-boundary actions, both in $x$-space and in superspace. For each standard supersymmetric bulk action a minimal supersymmetric bulk-plus-boundary action follows from an extended $F$- or $D$-term formula. Additional separately supersymmetric boundary actions can be systematically constructed using co-dimension one multiplets (boundary superfields). We also discuss the orbit of boundary conditions which follow from the Euler-Lagrange variational principle.Comment: 28 pages, JHEP clas

On solid ergodicity for Gaussian actions

We investigate Gaussian actions through the study of their crossed-product von Neumann algebra. The motivational result is Chifan and Ioana's ergodic decomposition theorem for Bernoulli actions (Ergodic subequivalence relations induced by a Bernoulli action, {\it Geometric and Functional Analysis}{\bf 20} (2010), 53-67) that we generalize to Gaussian actions. We also give general structural results that allow us to get a more accurate result at the level of von Neumann algebras. More precisely, for a large class of Gaussian actions $\Gamma \curvearrowright X$, we show that any subfactor $N$ of $L^\infty(X) \rtimes \Gamma$ containing $L^\infty(X)$ is either hyperfinite or is non-Gamma and prime. At the end of the article, we generalize this result to Bogoliubov actions.Comment: Updated version, 20 page