Abstract:
taking into account the historical perspective, i examine in this article the relation between a hindu mother-in-law and her daughter-in-law within a migration network involving diu (india), mozambique, portugal and england. my reflections are part of a research project on hindu families in mozambique, aimed at establishing a critical dialogue with those studies that see the hindu family in africa as a stronghold of identity for populations thought of as originally indian. inspired in the anthropological literature that emphasizes the time dimension of relational systems, i seek to underline, in the context of contemporary mozambique, the flexibility of hierarchies in which married indian women participate.

Abstract:
In this paper we derive in a coordinate-free manner the field equations for a lagrangean consisting of Yang-Mills kinetical term plus Chern-Simons self-coupling term. This equation turns out to be an eigenvalue equation for the covariant laplacian.

Abstract:
We construct finite energy instanton connection on $R^4$ which are periodic in two directions via an analogue of the Nahm transform for certain singular solutions of Hitchin's equations defined over a 2-torus.

Abstract:
We present the Nahm transform of the doubly-periodic instantons introduced in math.DG/9909069, converting them into certain meromorphic solutions of Hitchin's equations over an elliptic curve.

Abstract:
This work concerns the study of certain finite-energy solutions of the anti-self-dual Yang-Mills equations on Euclidean 4-dimensional space which are periodic in two directions, so-called doubly-periodic instantons. We establish a circle of ideas involving equivalent analytical and algebraic-geometric descriptions of these objects. In the first introductory chapter we provide an overview of the problem and state the main results to be proven in the thesis. In chapter 2, we study the asymptotic behaviour of the connections we are concerned with, and show that the coupled Dirac operator is Fredholm. After laying these foundations, we are ready to address the main topic of the thesis, the construction of a Nahm transform of doubly-periodic instantons. By combining differential-geometric and holomorphic methods, we show in chapters 3 through 5 that doubly-periodic instantons correspond bijectively to certain singular Higgs pairs, i.e. meromorphic solutions of Hitchin's equations defined over an elliptic curve. The circle of ideas is finally closed in chapter 8. We start by presenting a construction due to Friedman, Morgan and Witten that associates to each doubly-periodic instanton a spectral pair consisting of a Riemann surface plus a line bundle over it. On the other hand, it was shown by Hitchin that Higgs pairs are equivalent to a similar set of data. We show that the Friedman, Morgan and Witten spectral pair associated with a doubly-periodic instanton coincides with the Hitchin spectral pair associated with its Nahm transform. (This thesis contains the papers math.DG/9909069, math.DG/9910120 and math.AG/9909146.)

Abstract:
We present a 1-parameter family of finite action solutions to the $S0(2,1)$ Hitchin's equations and explore some of its basic properties. For a fixed value of the parameter, the solution is smooth. We conclude by showing a multi-particle generalization of our basic solutions.

Abstract:
This paper has been withdraw. A fully revised version with two new co-authors has been posted: "ADHM construction of perverse instanton sheaves", arXiv:1201.5657.

Abstract:
We present a classification of SU(2) instantons on $T^2\times\mathbb{R}^2$ according to their asymptotic behaviour. We then study the existence of such instantons for different values of the asymptotic parameters, describing explicitly the moduli space for unit charge.

Abstract:
We review the construction known as the Nahm transform in a generalized context, which includes all the examples of this construction already described in the literature. The Nahm transform for translation invariant instantons on $\real^4$ is presented in an uniform manner. We also analyze two new examples, the first of which being the first example involving a four-manifold that is not complex.

Abstract:
Using monads, we construct a large class of stable bundles of rank 2 and 3 on 3-fold hypersurfaces, and study the set of all possible Chern classes of stable vector bundles.