Who cried for Argentina? Notes on the 2001-02 Crisis

In the midst of the current global slowdown this paper revisits Argentina’s dismal experience in the 1990s with a complete embrace of globalisation, the crisis of 2001-02 and its subsequent recovery.Argentine; Economic; Crisis;

The role of the Beltrami parametrization of complex structures in 2-d Free Conformal Field Theory

This talk gives a review on how complex geometry and a Lagrangian formulation of 2-d conformal field theory are deeply related. In particular, how the use of the Beltrami parametrization of complex structures on a compact Riemann surface fits perfectly with the celebrated locality principle of field theory, the latter requiring the use infinite dimensional spaces. It also allows a direct application of the local index theorem for families of elliptic operators due to J.-M. Bismut, H. Gillet and C. Soul\'{e}. The link between determinant line bundles equipped with the Quillen\'s metric and the so-called holomorphic factorization property will be addressed in the case of free spin $j$ b-c systems or more generally of free fields with values sections of a holomorphic vector bundles over a compact Riemann surface.Comment: Actes du Colloque "Complex Geometry '98

Improved Epstein-Glaser Renormalization II. Lorentz invariant framework

The Epstein--Glaser type T-subtraction introduced by one of the authors in a previous paper is extended to the Lorentz invariant framework. The advantage of using our subtraction instead of Epstein and Glaser's standard W-subtraction method is especially important when working in Minkowski space, as then the counterterms necessary to keep Lorentz invariance are simplified. We show how T-renormalization of primitive diagrams in the Lorentz invariant framework directly relates to causal Riesz distributions. A covariant subtraction rule in momentum space is found, sharply improving upon the BPHZL method for massless theories.Comment: LaTeX, 15 pages, no figure. Version to be published in J. Math. Phys. (Section 7 on the Massive Case and some references have been withdrawn). To the Memory of Laurent Schwart

Gauge field theories: various mathematical approaches

This paper presents relevant modern mathematical formulations for (classical) gauge field theories, namely, ordinary differential geometry, noncommutative geometry, and transitive Lie algebroids. They provide rigorous frameworks to describe Yang-Mills-Higgs theories or gravitation theories, and each of them improves the paradigm of gauge field theories. A brief comparison between them is carried out, essentially due to the various notions of connection. However they reveal a compelling common mathematical pattern on which the paper concludes.Comment: 33 pages. To be published in the book: Mathematical Structures of the Universe (Copernicus Center Press, Krak\'ow, Poland, 2014

Local description of generalized forms on transitive Lie algebroids and applications

In this paper we study the local description of spaces of forms on transitive Lie algebroids. We use this local description to introduce global structures like metrics, $\ast$-Hodge operation and integration along the algebraic part of the transitive Lie algebroid (its kernel). We construct a \v{C}ech-de Rham bicomplex with a Leray-Serre spectral sequence. We apply the general theory to Atiyah Lie algebroids and to derivations on a vector bundle