Assumindo novas identidades: resistência indígena no litoral sul do Espírito Santo (século XVIII).

Na primeira metade do século XVI, a resistência indígena nesta e em outras capitanias deixou claro aos portugueses quão difícil seria a colonização dessas áreas. Diante desses desafios a Coroa Portuguesa adotou uma nova política, da qual fazia parte o envio de jesuítas para a América. Nesse contexto foram criadas no sul do Espírito Santo as missões de Guaraparim e Iriritiba. Nesta última, local de moradia do padre José de Anchieta em seus derradeiros anos de vida, a gravidade e amplitude de uma série de levantes iniciados no ano de 1742 deixaram sobressaltadas autoridades civis e religiosas. A notoriedade desta localidade e desses eventos, no entanto, não se refletiu na academia. Buscando contribuir para a mudança nesse panorama, começamos um processo de releitura de obras sobre a história do Espírito Santo e de correspondências oficiais sobre as revoltas utilizando conceitos como circularidade cultural, hibridismo, mestiçagem e etnogênese impressos nos textos de autores como Carlo Ginzburg, Guillaume Boccara, John Manuel Monteiro, Ronaldo Vainfas, Eduardo Viveiros de Castro, Manuela Carneiro da Cunha, Michel de Certeau e Maria Regina Celestino de Almeida. A princípio constatamos que apesar do esforço daqueles autores em apresentarem uma narrativa dual, que acondicionava colonizados e colonizadores em compartimentos estanques, seus textos traziam indícios que contrariavam essa representação simplista. Pensamento consolidado com a publicação do Auto da Devassa de 1761, ação organizada pelo Santo Ofício para apurar supostas irregularidades cometidas pelos inacianos durante sua permanência nesta capitania. Ao reproduzir o depoimento de índios que viviam em Guaraparim, Iriritiba e no Orobó, o documento nos apresentou indivíduos com trajetórias impensáveis para os modelos dicotômicos anteriores. Pessoas que para sobreviverem a todas aquelas transformações reinventaram-se repetidas vezes, criando e assumindo diferentes identidades. Uma parte deles, uma vez alijada dos cargos de administração da aldeia, migrou para o vale do Orobó fundando uma aldeia onde viveram, como sugeria o nome por eles escolhido, à eles, para eles, com a exclusão deles

Surgery and the Spectrum of the Dirac Operator

We show that for generic Riemannian metrics on a simply-connected closed spin manifold of dimension at least 5 the dimension of the space of harmonic spinors is no larger than it must be by the index theorem. The same result holds for periodic fundamental groups of odd order. The proof is based on a surgery theorem for the Dirac spectrum which says that if one performs surgery of codimension at least 3 on a closed Riemannian spin manifold, then the Dirac spectrum changes arbitrarily little provided the metric on the manifold after surgery is chosen properly.Comment: 23 pages, 4 figures, to appear in J. Reine Angew. Mat

Generic metrics and the mass endomorphism on spin three-manifolds

Let $(M,g)$ be a closed Riemannian spin manifold. The constant term in the expansion of the Green function for the Dirac operator at a fixed point $p\in M$ is called the mass endomorphism in $p$ associated to the metric $g$ due to an analogy to the mass in the Yamabe problem. We show that the mass endomorphism of a generic metric on a three-dimensional spin manifold is nonzero. This implies a strict inequality which can be used to avoid bubbling-off phenomena in conformal spin geometry.Comment: 8 page

The Dirac operator on generalized Taub-NUT spaces

We find sufficient conditions for the absence of harmonic $L^2$ spinors on spin manifolds constructed as cone bundles over a compact K\"ahler base. These conditions are fulfilled for certain perturbations of the Euclidean metric, and also for the generalized Taub-NUT metrics of Iwai-Katayama, thus proving a conjecture of Vi\csinescu and the second author.Comment: Final version, 16 page

A Reilly formula and eigenvalue estimates for differential forms

We derive a Reilly-type formula for differential p-forms on a compact manifold with boundary and apply it to give a sharp lower bound of the spectrum of the Hodge Laplacian acting on differential forms of an embedded hypersurface of a Riemannian manifold. The equality case of our inequality gives rise to a number of rigidity results, when the geometry of the boundary has special properties and the domain is non-negatively curved. Finally we also obtain, as a by-product of our calculations, an upper bound of the first eigenvalue of the Hodge Laplacian when the ambient manifold supports non-trivial parallel forms.Comment: 22 page

On a spin conformal invariant on manifolds with boundary

On a n-dimensional connected compact manifold with non-empty boundary equipped with a Riemannian metric, a spin structure and a chirality operator, we study some properties of a spin conformal invariant defined from the first eigenvalue of the Dirac operator under the chiral bag boundary condition. More precisely, we show that we can derive a spinorial analogue of Aubin's inequality.Comment: 26 page

Vacuum Spacetimes with Future Trapped Surfaces

In this article we show that one can construct initial data for the Einstein equations which satisfy the vacuum constraints. This initial data is defined on a manifold with topology $R^3$ with a regular center and is asymptotically flat. Further, this initial data will contain an annular region which is foliated by two-surfaces of topology $S^2$. These two-surfaces are future trapped in the language of Penrose. The Penrose singularity theorem guarantees that the vacuum spacetime which evolves from this initial data is future null incomplete.Comment: 19 page

Vanishing Viscous Limits for 3D Navier-Stokes Equations with A Navier-Slip Boundary Condition

In this paper, we investigate the vanishing viscosity limit for solutions to the Navier-Stokes equations with a Navier slip boundary condition on general compact and smooth domains in $\mathbf{R}^3$. We first obtain the higher order regularity estimates for the solutions to Prandtl's equation boundary layers. Furthermore, we prove that the strong solution to Navier-Stokes equations converges to the Eulerian one in $C([0,T];H^1(\Omega))$ and L^\infty((0,T)\times\o), where $T$ is independent of the viscosity, provided that initial velocity is regular enough. Furthermore, rates of convergence are obtained also.Comment: 45page

Changes in electrophysiological static and dynamic human brain functional architecture from childhood to late adulthood

Published: 04 November 2020This magnetoencephalography study aimed at characterizing age-related changes in resting-state functional brain organization from mid-childhood to late adulthood. We investigated neuromagnetic brain activity at rest in 105 participants divided into three age groups: children (6–9 years), young adults (18–34 years) and healthy elders (53–78 years). The effects of age on static resting-state functional brain integration were assessed using band-limited power envelope correlation, whereas those on transient functional brain dynamics were disclosed using hidden Markov modeling of power envelope activity. Brain development from childhood to adulthood came with (1) a strengthening of functional integration within and between resting-state networks and (2) an increased temporal stability of transient (100–300 ms lifetime) and recurrent states of network activation or deactivation mainly encompassing lateral or medial associative neocortical areas. Healthy aging was characterized by decreased static resting-state functional integration and dynamic stability within the primary visual network. These results based on electrophysiological measurements free of neurovascular biases suggest that functional brain integration mainly evolves during brain development, with limited changes in healthy aging. These novel electrophysiological insights into human brain functional architecture across the lifespan pave the way for future clinical studies investigating how brain disorders affect brain development or healthy aging.This study was supported by the Action de Recherche Concertée Consolidation (ARCC, “Characterizing the spatio-temporal dynamics and the electrophysiological bases of resting state networks”, ULB, Brussels, Belgium), the Fonds Erasme (Research Convention “Les Voies du Savoir”,Brussels, Belgium) and the Fonds de la Recherche Scientifique (Research Convention: T.0109.13, FRS-FNRS, Brussels, Belgium). Nicolas Coquelet has been supported by the ARCC, by the Fonds Erasme (Research Convention “Les Voies du Savoir”, Brussels, Belgium) and is supported by the FRS-FNRS (Research Convention: Excellence of Science EOS “MEMODYN”). Alison Mary is Postdoctoral Researcher at the FRS-FNRS. Maxime Niesen and Marc Vander Ghinst have been supported by the Fonds Erasme. Mariagrazia Ranzini is supported by the Marie Sklodowska-Curie European Union’s Horizon 2020 research and innovation program (Research Grant: 839394). Mathieu Bourguignon is supported by the program Attract of Innoviris (Research Grant 2015-BB2B-10, Brussels, Belgium), the Marie Sklodowska-Curie Action of the European Commission (Research Grant: 743562) and by the Spanish Ministery of Economy and Competitiveness (Research Grant: PSI2016-77175-P). Xavier De Tiège is Postdoctorate Clinical Master Specialist at the FRS-FNRS. The MEG project at the CUB Hôpital Erasme is financially supported by the Fonds Erasme