Pure motives, mixed motives and extensions of motives associated to singular surfaces

We first recall the construction of the Chow motive modelling intersection cohomology of a proper surface X and study its fundamental properties. Using Voevodsky's category of effective geometrical motives, we then study the motive of the exceptional divisor D in a non-singular blow-up of X. If all geometric irreducible components of D are of genus zero, then Voevodsky's formalism allows us to construct certain one-extensions of Chow motives, as canonical subquotients of the motive with compact support of the smooth part of X. Specializing to Hilbert-Blumenthal surfaces, we recover a motivic interpretation of a recent construction of A. Caspar.

Hopf bifurcation for degenerate singular points of multiplicity 2n-1 in dimension 3

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Shelah's singular compactness theorem

We present Shelah’s famous theorem in a version for modules, together with a self-contained proof and some examples. This exposition is based on lectures given at CRM in October 2006.

Convergence of singular integrals with general measures

We show that L2-bounded singular integrals in metric spaces with respect to general measures and kernels converge weakly. This implies a kind of average convergence almost everywhere. For measures with zero density we prove the almost everywhere existence of principal values.

On the boundedness on inhomogeneous Lipschitz spaces of fractional integrals, singular integrals and hypersingular integrals associated to non-doubling measures on metric spaces

In this paper we prove T1 type necessary and sufficient conditions for the boundedness on inhomogeneous Lipschitz spaces of fractional integrals and singular integrals defined on a measure metric space whose measure satisfies a n-dimensional growth. We also show that hypersingular integrals are bounded on these spaces.

New estimates for the maximal singular integral

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Mujeres en la casa, la escuela y la fábrica. El singular discurso de la domesticidad de la escuela economista española (1861-1909)

Los textos de la Escuela Economista Española (segunda mitad del XIX) contienen una valoración del papel de las mujeres en la economía y la sociedad transgresor frente al discurso dominante, que defendía un único y exclusivo rol para todas las mujeres: el hogar y la maternidad. La mayoría de los miembros de esta corriente económica defienden el trabajo femenino en las fábricas, basándose en argumentos salariales; e incluso demandan una formación profesional para aquellas que en muchos casos ni tan siquiera eran alfabetizadas por ser mujeres. Los textos de estos economistas transmiten nuevas ideas sobre el papel económico y social de las mujeres en una España dominada por un discurso que negaba la necesidad del trabajo femenino para las familias trabajadoras.

Singular integrals on Ahlfors-David regular subsets of the Heisenberg group

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A characterization of two weight norm inequalities for maximal singular integrals

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Bergman-type singular operators and the characterization of Carleson measures for Besov-Sobolev spaces on the complex ball

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Singular Bott-Chern classes and the arithmetic Grothendieck-Riemann-Roch theorem for closed immersions

We study the singular Bott-Chern classes introduced by Bismut, Gillet and Soulé. Singular Bott-Chern classes are the main ingredient to define direct images for closed immersions in arithmetic K-theory. In this paper we give an axiomatic definition of a theory of singular Bott-Chern classes, study their properties, and classify all possible theories of this kind. We identify the theory defined by Bismut, Gillet and Soulé as the only one that satisfies the additional condition of being homogeneous. We include a proof of the arithmetic Grothendieck-Riemann-Roch theorem for closed immersions that generalizes a result of Bismut, Gillet and Soulé and was already proved by Zha. This result can be combined with the arithmetic Grothendieck-Riemann-Roch theorem for submersions to extend this theorem to arbitrary projective morphisms. As a byproduct of this study we obtain two results of independent interest. First, we prove a Poincaré lemma for the complex of currents with fixed wave front set, and second we prove that certain direct images of Bott-Chern classes are closed.

Homologia de Lawson i descens

La meva recerca en els tres anys de gaudiment de beca s'ha centrat en l'estudi de teories semitopològiques definides a través d'espais de cicles algebraics, introduïts per Friedlander i Lawson. Hem estudiat propietats de descens d'aquestes teories i hem construït una successió espectral que calcula explícitament la cohomologia mòrfica d'una varietat tòrica. D'altra banda, estem treballant en l'estudi de propietats d'invariància homotòpica per la cohomologia mòrfica, així com en l'estructura algebraica dels grups d'homologia de Lawson.

La Selva: una comarca singular per la seva heterogeneïtat

Sobre el creixement urbà, el desenvolupament i l'ordenació territorial de La Selva, comarca singular per la seva heterogeneïtat

Constraint algorithm for k-presymplectic Hamiltonian systems. Application to singular field theories

The k-symplectic formulation of field theories is especially simple, since only tangent and cotangent bundles are needed in its description. Its defining elements show a close relationship with those in the symplectic formulation of mechanics. It will be shown that this relationship also stands in the presymplectic case. In a natural way,one can mimick the presymplectic constraint algorithm to obtain a constraint algorithmthat can be applied to k-presymplectic field theory, and more particularly to the Lagrangian and Hamiltonian formulations offield theories defined by a singular Lagrangian, as well as to the unified Lagrangian-Hamiltonian formalism (Skinner--Rusk formalism) for k-presymplectic field theory. Two examples of application of the algorithm are also analyzed.

Del tenir al ser: un camí per a fer junts : Una anàlisi singular des de l'escola

El treball tracta sobre l'ús de les noves tecnologies entre els adolescents i la relació que s'en deriva a l'escola, la família i la societat en general.