On the classification of pointed fusion categories up to weak Morita equivalence

A pointed fusion category is a rigid tensor category with finitely many isomorphism classes of simple objects which moreover are invertible. Two tensor categories $C$ and $D$ are weakly Morita equivalent if there exists an indecomposable right module category $M$ over $C$ such that $Fun_C(M,M)$ and $D$ are tensor equivalent. We use the Lyndon-Hochschild-Serre spectral sequence associated to abelian group extensions to give necessary and sufficient conditions in terms of cohomology classes for two pointed fusion categories to be weakly Morita equivalent. This result may permit to classify the equivalence classes of pointed fusion categories of any given global dimension.Comment: Corrected version. Accepted for publication in PJM. 26 page

Chern-Weil homomorphism in twisted equivariant cohomology

AbstractWe describe the Cartan and Weil models of twisted equivariant cohomology together with the Cartan homomorphism among the two, and we extend the Chern–Weil homomorphism to the twisted equivariant cohomology. We clarify that in order to have a cohomology theory, the coefficients of the twisted equivariant cohomology must be taken in the completed polynomial algebra over the dual Lie algebra of G. We recall the relation between the equivariant cohomology of exact Courant algebroids and the twisted equivariant cohomology, and we show how to endow with a generalized complex structure the finite-dimensional approximations of the Borel construction M×GEGk, whenever the generalized complex manifold M possesses a Hamiltonian G-action

Sulfur loss from subducted altered oceanic crust and implications for mantle oxidation

© The Author(s), [year]. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Walters, J. B., Cruz-Uribe, A. M., & Marschall, H. R. Sulfur loss from subducted altered oceanic crust and implications for mantle oxidation. Geochemical Perspectives Letters, 13, (2020): 36-41, doi:10.7185/geochemlet.2011.Oxygen fugacity (fO2) is a controlling factor of the physics of Earth’s mantle; however, the mechanisms driving spatial and secular changes in fO2 associated with convergent margins are highly debated. We present new thermodynamic models and petrographic observations to predict that oxidised sulfur species are produced during the subduction of altered oceanic crust. Sulfur loss from the subducting slab is a function of the protolith Fe3+/ΣFe ratio and subduction zone thermal structure, with elevated sulfur fluxes predicted for oxidised slabs in cold subduction zones. We also predict bi-modal release of sulfur-bearing fluids, with a low volume shallow flux of reduced sulfur followed by an enhanced deep flux of sulfate and sulfite species, consistent with oxidised arc magmas and associated copper porphyry deposits. The variable SOx release predicted by our models both across and among active margins may introduce fO2 heterogeneity to the upper mantle.We thank James Connolly for modelling support and Peter van Keken for providing updated P–T paths for the Syracuse et al. (2010) models. The manuscript benefited from the editorial handling by Helen Williams and from constructive reviews of Maryjo Brounce, Katy Evans, and an anonymous reviewer. JBW acknowledges Fulbright and Chase Distinguished Research fellowships. This work was supported by NSF grant EAR1725301 awarded to AMC

La percepciópn cultural de la experiencia migrante

[Resumen] Con los procesos de globalización económica, las relaciones laborales y las percepciones simbólicas de la cultura se construyen cada vez más a partir de los procesos migratorios. Es el caso de los trabajadores mexicanos en Estados Unidos. El Programa Bracero (1942/1964) fue una estrategia que buscó proveer de condiciones legales a miles de trabajadores mexicanos en los campos agrícolas y del ferrocarril en Estados Unidos. Como trabajo temporal, muchos migrantes regresaron a sus lugares de origen en México una vez concluidos los contratos. El objetivo de esta ponencia es discutir la percepción y valoración simbólica de la experiencia migrante de los trabajadores pertenecientes al Programa Bracero. Interesa reflexionar en términos de la propia subjetividad e identidad del exbracero, para saber, cómo se representan el sentido del éxito o fracaso de la experiencia cultural en el extranjero, cómo perciben a sí mismos sus capacidades de adaptación laboral. Como fuente primaria, este trabajo se apoyará en una investigación de carácter cualitativo realizada con ex braceros en el estado de Colima, México, y como fuente secundaria una encuesta realizada también con el mismo fin. Los estudios sobre migración internacional con énfasis en mexicanos en Estados Unidos, se han enfatizado más en el aspecto económico y demográfico de los migrantes, pero no en el cultural simbólico. En ese sentido, esta ponencia pretende retomar desde la perspectiva de los estudios culturales y la semiótica de la cultura la experiencia migrante

Expanding School Enrollment by Subsidizing Private Schools: Lessons from Bogotá

Many countries use tax revenues to subsidize private schools. Whether these policies meet social objectives depends, in part, on the relative quality of education provided by the two types of schools. We use data on elementary school students and their teachers in Bogotá, Colombia to examine difference in resource mixes and differences in the relative effectiveness of public and private schools. We find that, on average, the schools in the two sectors are equally effective. However, they produce education using very different resource combinations. Moreover, there are large differences in the effectiveness of schools in both sectors, especially in the private sector. The results of our analysis shed light on the quantity-quality tradeoff that governments in many developing countries face in deciding how to use scarce educational resources.

Weighted Sobolev theorem with variable exponent for spatial and spherical potential operators

We prove Sobolev-type p((.)) -> q ((.))-theorems for the Riesz potential operator I-alpha in the weighted Lebesgue generalized spaces L-p(.)(R-n, p) with the variable exponent p (x) and a two-parametrical power weight fixed to an arbitrary finite point and to infinity, as well as similar theorems for a spherical analogue of the Riesz potential operator in the corresponding weighted spaces L-p(.)(S-n, p) on the unit sphere S-n in Rn+1. (c) 2005 Elsevier Inc. All rights reserved.info:eu-repo/semantics/publishedVersio

Classification of pointed fusion categories of dimension p3p^3 up to weak Morita equivalence

We give a complete classification of pointed fusion categories over $\mathbb{C}$ of global dimension $p^3$ for $p$ any odd prime. We proceed to classify the equivalence classes of pointed fusion categories of dimension $p^3$ and we determine which of these equivalence classes have equivalent categories of modules

Quasinodal lines in rhombohedral magnetic materials

A well-established result in condensed matter physics states that materials crystallizing in symmetry groups containing glide reflection symmetries possess nodal lines on the energy bands. These nodal lines are topologically protected and appear on the fixed planes of the reflection in reciprocal space. In the presence of inversion symmetry, the energy bands are degenerate and the band crossings on the fixed plane may be one-dimensional, or may intersect in points, including the case of empty intersection. In the latter case, the crossing is partially or totally avoided, thus producing lines on reciprocal space where the energy gap may be small, and in the former, the nodal lines will endure, thus producing Dirac or double nodal lines. In addition, if the material crystallizes in a ferromagnetic phase where the glide reflection symmetry is broken, the nodal lines hybridize, thus defining lines in reciprocal space where the energy gap may be small. In this work, we concentrate our efforts on the study of nodal lines that hybridize due to magnetization; we have coined the term of quasinodal lines for those lines in reciprocal space where the energy gap is small (less than what can be detected experimentally ∼25 meV). We study magnetic trifluorides and trioxides which crystallize in magnetic space groups 167.107 and 161.71 and we show the existence of quasinodal lines on these materials. We furthermore show that whenever the quasinodal lines are located around the Fermi level then interesting charge and spin transport effects are induced and can be used to detect experimentally these lines. Of particular interest are the half-metallic ferromagnetic phases of PdF3 and LiCuF3 where the large signal of the anomalous Hall conductance is due to the presence of the quasinodal lines on the Fermi level