Membrane Sigma-Models and Quantization of Non-Geometric Flux Backgrounds

We develop quantization techniques for describing the nonassociative geometry probed by closed strings in flat non-geometric R-flux backgrounds M. Starting from a suitable Courant sigma-model on an open membrane with target space M, regarded as a topological sector of closed string dynamics in R-space, we derive a twisted Poisson sigma-model on the boundary of the membrane whose target space is the cotangent bundle T^*M and whose quasi-Poisson structure coincides with those previously proposed. We argue that from the membrane perspective the path integral over multivalued closed string fields in Q-space is equivalent to integrating over open strings in R-space. The corresponding boundary correlation functions reproduce Kontsevich's deformation quantization formula for the twisted Poisson manifolds. For constant R-flux, we derive closed formulas for the corresponding nonassociative star product and its associator, and compare them with previous proposals for a 3-product of fields on R-space. We develop various versions of the Seiberg-Witten map which relate our nonassociative star products to associative ones and add fluctuations to the R-flux background. We show that the Kontsevich formula coincides with the star product obtained by quantizing the dual of a Lie 2-algebra via convolution in an integrating Lie 2-group associated to the T-dual doubled geometry, and hence clarify the relation to the twisted convolution products for topological nonassociative torus bundles. We further demonstrate how our approach leads to a consistent quantization of Nambu-Poisson 3-brackets.Comment: 52 pages; v2: references adde

Lectures on Nongeometric Flux Compactifications

These notes present a pedagogical review of nongeometric flux compactifications. We begin by reviewing well-known geometric flux compactifications in Type II string theory, and argue that one must include nongeometric "fluxes" in order to have a superpotential which is invariant under T-duality. Additionally, we discuss some elementary aspects of the worldsheet description of nongeometric backgrounds. This review is based on lectures given at the 2007 RTN Winter School at CERN.Comment: 31 pages, JHEP

On twisted Fourier analysis and convergence of Fourier series on discrete groups

We study norm convergence and summability of Fourier series in the setting of reduced twisted group $C^*$-algebras of discrete groups. For amenable groups, F{\o}lner nets give the key to Fej\'er summation. We show that Abel-Poisson summation holds for a large class of groups, including e.g. all Coxeter groups and all Gromov hyperbolic groups. As a tool in our presentation, we introduce notions of polynomial and subexponential H-growth for countable groups w.r.t. proper scale functions, usually chosen as length functions. These coincide with the classical notions of growth in the case of amenable groups.Comment: 35 pages; abridged, revised and update

Translation and Memory Across Cultures and Disciplines. Past and future tenses

The relationship between translation and memory has very much to do with not only the position of the person who is translating, but also with that of the person who is writing about translation, and thus creating an archive\u2013memory of all the lives a text might have, along with its histories and narratives, its former and new translated meanings. If all critical analysis and meditation on the differences between languages\u2014which includes the memory that sustains them, and the memory-texts in the languages that manage to survive\u2014are but a translation/self-translation, often erasing nuances and disregarding untranslatability, then in which recesses of translation (from and into English and into every other language) and memory does the future of the humanities reside

Amenable actions, invariant means and bounded cohomology

We show that topological amenability of an action of a countable discrete group on a compact spaceis equivalent to the existence of an invariant mean for the action. We prove also that this is equivalent to vanishing ofbounded cohomology for a class of Banach G-modules associated to the action, as well as to vanishing of a specific cohomology class. In the case when the compact space is a point our result reduces to a classic theorem of B.E.~Johnson characterising amenability of groups. In the case when the compactspace is the Stone-\v{C}ech compactification of the group we obtain a cohomological characterisation of exactness for the group, answering a question of Higson

Long-term subclinical copper deficiency and it is influence on functions of parenchymal organs and the serum macro-element deficiency in dairy cows

Copper deficiency is a mineral management disorder increasingly often diagnosed in dairy cattle herds in Poland. Diagnosis of this disorder in herds can be very difficult as subclinical deficiencies may occur over long periods of time without clear clinical symptoms. Subclinical or atypical deficiencies that long remain untreated cause major disturbances in homeostasis. Information is scarce in the literature about the changes that occur in biochemical blood parameters in the course of atypical long-term subclinical copper deficiency. This study was conducted on a group of 80 cows from farms in the central part of the Lublin region in Poland. The animals were divided into four groups: three groups with Cu deficiency (two of these groups did not receive preventive supplementation, and the third one had oral copper supplementation administered) and a control group (clinically healthy cows). Blood for the tests was collected in the same period, 6 and 12 weeks after calving and a year after the previous tests. The results obtained in the groups where no special preventive measures had been taken showed a negative influence of copper deficiency on the functional condition of organs, especially the liver and pancreas (in the final stage of the study), and on blood phosphorus concentration. Such findings were not observed in the group supplemented with a copper-rich feed additive. In this group, after only a month of being supplemented with a preparation containing copper, a 15% increase in milk yield was observed. Meanwhile, the milk yield decreased in the remaining groups

Long-term subclinical copper deficiency and it is influence on functions of parenchymal organs and the serum macro-element deficiency in dairy cows

Copper deficiency is a mineral management disorder increasingly often diagnosed in dairy cattle herds in Poland. Diagnosis of this disorder in herds can be very difficult as subclinical deficiencies may occur over long periods of time without clear clinical symptoms. Subclinical or atypical deficiencies that long remain untreated cause major disturbances in homeostasis. Information is scarce in the literature about the changes that occur in biochemical blood parameters in the course of atypical long-term subclinical copper deficiency. This study was conducted on a group of 80 cows from farms in the central part of the Lublin region in Poland. The animals were divided into four groups: three groups with Cu deficiency (two of these groups did not receive preventive supplementation, and the third one had oral copper supplementation administered) and a control group (clinically healthy cows). Blood for the tests was collected in the same period, 6 and 12 weeks after calving and a year after the previous tests. The results obtained in the groups where no special preventive measures had been taken showed a negative influence of copper deficiency on the functional condition of organs, especially the liver and pancreas (in the final stage of the study), and on blood phosphorus concentration. Such findings were not observed in the group supplemented with a copper-rich feed additive. In this group, after only a month of being supplemented with a preparation containing copper, a 15% increase in milk yield was observed. Meanwhile, the milk yield decreased in the remaining groups