The Zariski-Lefschetz principle for higher homotopy groups of nongeneric pencils

We prove a general Zariski-van Kampen-Lefschetz type theorem for higher homotopy groups of generic and nongeneric pencils on singular open complex spaces.

Some things couples always wanted to know about stable matchings (but were afraid to ask)

It is well-known that couples that look jointly for jobs in the same centralized labor market may cause instabilities. We demonstrate that for a natural preference domain for couples, namely the domain of responsive preferences, the existence of stable matchings can easily be established. However, a small deviation from responsiveness in one couple's preference relation that models the wish of a couple to be closer together may already cause instability. This demonstrates that the nonexistence of stable matchings in couples markets is not a singular theoretical irregularity. Our nonexistence result persists even when a weaker stability notion is used that excludes myopic blocking. Moreover, we show that even if preferences are responsive there are problems that do not arise for singles markets. Even though for couples markets with responsive preferences the set of stable matchings is nonempty, the lattice structure that this set has for singles markets does not carry over. Furthermore we demonstrate that the new algorithm adopted by the National Resident Matching Program to fill positions for physicians in the United States may cycle, while in fact a stable matchings does exist, and be prone to strategic manipulation if the members of a couple pretend to be single.

Intersection Pairing and intersection motive of surfaces

We construct the Chow motive modelling intersection co-homology of a proper surface. We then study its functoriality properties. Using Murre's decompositions of the motive of a desingularization into KÄunneth components [Mr1], we show that such decompositions exist also for the intersection motive.

Non compact euclidean cone 3-manifolds with cone angles less than 2∏

We study of noncompact Euclidean cone manifolds with cone angles less than c&2π and singular locus a submanifold. More precisely, we describe its structure outside a compact set. As a corol lary we classify those with cone angles & 2π/3 and those with cone angles = 2π/3.

Traverso's isogeny conjecture for p-divisible groups

"Vegeu el resum a l'inici del document adjunt."

Semipurity of tempered Deligne cohomology

In this paper we define the formal and tempered Deligne cohomology groups, that are obtained by applying the Deligne complex functor to the complexes of formal differential forms and tempered currents respectively. We then prove the existence of a duality between them, a vanishing theorem for the former and a semipurity property for the latter. The motivation of this results comes from the study of covariant arithmetic Chow groups. The semi-purity property of tempered Deligne cohomology implies, in particular, that several definitions of covariant arithmetic Chow groups agree for projective arithmetic varieties.

Variational inequalities in Hilbert spaces with measures and optimal stopping problems

We study the existence theory for parabolic variational inequalities in weighted L2 spaces with respect to excessive measures associated with a transition semigroup. We characterize the value function of optimal stopping problems for finite and infinite dimensional diffusions as a generalized solution of such a variational inequality. The weighted L2 setting allows us to cover some singular cases, such as optimal stopping for stochastic equations with degenerate diffusion coeficient. As an application of the theory, we consider the pricing of American-style contingent claims. Among others, we treat the cases of assets with stochastic volatility and with path-dependent payoffs.

Cosa: arqueologia de un enclave comercial mediterráneo. Campaña de 2006

En el marco del proyecto “La ciutat romana de Cosa: arqueologia d’un enclau comercial mediterrani” , autorizado y apoyado por la Soprintendenza Archeologica por la Toscana, entre los dias 4 y 22 de septiembre de 2006 se ha realizado la segunda campaña de intervenciones arqueológicas en la ciudad romana de Cosa (Ansedonia, prov. Grosseto, Itàlia), colonia latina fundada en el 273 aC a unos 120 km. al norte de Roma. De acuerdo a los resultados obtenidos en la campanya del 2005 (localización/verificación de los límites precisos de la ínsula O-P/4-5 mediante la aplicación de técnicas de prospección geofísica completadas con la limpieza, registro y documentación arqueológica de las estructuras localizadas ) los trabajos del 2006 se han orientado hacia la identificación de la organización interna de la dicha ínsula tomando como referente el criptopórtico situado en el extremo N.E., el cual parece constituir el límite de una estructura singular (privada o pública ) estratégicamente ubicada en relación al fórum i a la Via Sacra. El trabajo de campo ha consistido en un intenso decapage con la finalidad de delimitar unidades de habitación complejas funcionalmente definidas y así la articulación existente entre ellas; en este sentido se ha podido documentar evidencias del espacio porticado superpuesto al criptopórtico así como, paralelamente a la calle 5 y en dirección a la Via Sacra, parte de habitaciones algunas de las cuales conservaban restos del pavimiento original, en un caso de mosaico. Paralelamente, se ha realizado el análisis en laboratorio de los materiales recuperados los cuales, aún procediendo de nivel superficial, empiezan a proporcionar datos sobre los diferentes momentos de ocupación de la zona, básicamente tardorepublicanos y augustales.

Inverse problems for invariant algebraic curves: explicit computations

Given an algebraic curve in the complex affine plane, we describe how to determine all planar polynomial vector fields which leave this curve invariant. If all (finite) singular points of the curve are nondegenerate, we give an explicit expression for these vector fields. In the general setting we provide an algorithmic approach, and as an alternative we discuss sigma processes.

Note on homology of expanding foliations

This note contains some remarks about the homologies that can be associated to a foliation which is invariant and uniformly expanded by a diffeomorphism. We construct a family of 'dynamical' closed currents supported on the foliation which help us relate the geometric volume growth of the leaves under the diffeomorphism with the map induced on homology in the case when these currents have nonzero homology.

Formal deformations of Poisson structures in low dimensions

In this paper, we study formal deformations of Poisson structures, especially for three families of Poisson varieties in dimensions two and three. For these families of Poisson structures, using an explicit basis of the second Poisson cohomology space, we solve the deformation equations at each step and obtain a large family of formal deformations for each Poisson structure which we consider. With the help of an explicit formula, we show that this family contains, modulo equivalence, all possible formal eformations. We show moreover that, when the Poisson structure is generic, all members of the family are non-equivalent.

Homotopy Batalin-Vilkovisky algebras

This paper provides an explicit cofibrant resolution of the operad encoding Batalin-Vilkovisky algebras. Thus it defines the notion of homotopy Batalin-Vilkovisky algebras with the required homotopy properties. To define this resolution we extend the theory of Koszul duality to operads and properads that are defined by quadratic and linear relations. The operad encoding Batalin-Vilkovisky algebras is shown to be Koszul in this sense. This allows us to prove a Poincaré-Birkhoff-Witt Theorem for such an operad and to give an explicit small quasi-free resolution for it. This particular resolution enables us to describe the deformation theory and homotopy theory of BV-algebras and of homotopy BV-algebras. We show that any topological conformal field theory carries a homotopy BV-algebra structure which lifts the BV-algebra structure on homology. The same result is proved for the singular chain complex of the double loop space of a topological space endowed with an action of the circle. We also prove the cyclic Deligne conjecture with this cofibrant resolution of the operad BV. We develop the general obstruction theory for algebras over the Koszul resolution of a properad and apply it to extend a conjecture of Lian-Zuckerman, showing that certain vertex algebras have an explicit homotopy BV-algebra structure.

Els primers llums del Delta

Treball de recerca realitzat per un alumne d'ensenyament secundari i guardonat amb un Premi CIRIT per fomentar l'esperit científic del Jovent l'any 2009. El treball és un estudi de l’evolució, tan tècnica com estètica dels fars paral•lela als avenços tecnològics i prenent com a protagonistes els singulars fars de ferro que es varen construir durant la segona meitat del segle XIX i varen funcionar durant un llarguíssim període en el delta de l’Ebre. L’estructura de ferro, ancorada directament sobre les sorres del delta va donar un caràcter especial a aquestes construccions que, d’altra banda, constituïen una tipologia única a Catalunya i a Espanya. Aquests fars van rebre el nom del lloc on foren ubicats estratègicament. De sud a nord: far de la Banya, far de Buda i far del Fangar. Els van projectar conjuntament, es van encendre per primera vegada el mateix dia, van ser l’habitatge dels seus faroners, van anar evolucionant tècnicament tots tres però el final de cadascun d’ells va ser molt diferent. La història dels fars de ferro ha anat lligada al paisatge i la vida d’aquestes singulars terres del Delta i després de més d’un segle de servei foren substituïts per altres que estèticament i tècnicament res tenen a veure amb els seus antecessors.

Sobolev mappings, degree, homotopy classes and rational homology spheres

"Vegeu el resum a l'inici del document del fitxer adjunt."

Un aspecte semàntic dels termes generals : la rigidesa

L'objectiu de la recerca és determinar quina és la noció de rigidesa més adient per als termes generals. Els termes generals són els que, per oposició als termes singulars, es poden aplicar a més d'un individu o exemplar, com per exemple 'tigre', 'aigua', 'bolígraf'. Des de Kripke es considera que alguns termes singulars, com els noms propis, són rígids. Un terme singular és rígid quan designa el mateix individu o objecte en tot món possible. Així 'Sòcrates' és un terme rígid perquè designa el mateix individu, Sòcrates, en tota circumstància contrafàctica. Kripke va proposar que alguns termes generals, com els termes de gènere natural, tals com 'aigua', 'calor' o 'tigre' també són rígids, però no va donar cap formulació precisa de la rigidesa per a termes generals. Des de llavors s'han proposat bàsicament dues concepcions de la rigidesa per a aquests termes: la que els considera designadors rígids i la que els considera aplicadors rígids. L'anàlisi de les dues concepcions pretén determinar quina és la millor comprensió de la rigidesa per a aquests termes, resultant la concepció dels aplicadors rígids indesitjable fonamentalment pels seus compromisos metafísics i allunyats de la semàntica.