On the asymptotic expansion of the colored Jones polynomial for torus knots

In the asymptotic expansion of the hyperbolic specification of the colored Jones polynomial of torus knots, we identify different geometric contributions, in particular Chern-Simons invariant and Reidemeister torsion.

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.

A foundation model for marxian breakdown theories based on a new falling rate of profit mechanism (Long version)

The paper presents a foundation model for Marxian theories of the breakdown of capitalism based on a new falling rate of profit mechanism. All of these theories are based on one or more of "the historical tendencies": a rising capital-wage bill ratio, a rising capitalist share and a falling rate of profit. The model is a foundation in the sense that it generates these tendencies in the context of a model with a constant subsistence wage. The newly discovered generating mechanism is based on neo-classical reasoning for a model with land. It is non-Ricardian in that land augmenting technical progress can be unboundedly rapid. Finally, since the model has no steady state, it is necessary to use a new technique, Chaplygin's method, to prove the result.

A foundation model for marxian breakdown theories based on a new falling rate of profit mechanism.

The paper presents a foundation model for Marxian theories of the breakdown of capitalism based on a new falling rate of profit mechanism. All of these theories are based on one or more of ?the historical tendencies?: a rising capital-wage bill ratio, a rising capitalist share and a falling rate of profit. The model is a foundation in the sense that it generates these tendencies in the context of a model with a constant subsistence wage. The newly discovered generating mechanism is based on neo-classical reasoning for a model with land. It is non-Ricardian in that land augmenting technical progress can be unboundedly rapid. Finally, since the model has no steady state, it is necessary to use a new technique, Chaplygin?s method, to prove the result.

A foundation model for marxian theories of the breakdown of capitalism

Marx and the writers that followed him have produced a number of theories of the breakdown of capitalism. The majority of these theories were based on the historical tendencies: the rise in the composition of capital and the share of capital and the fall in the rate of profit. However these theories were never modeled with main stream rigour. This paper presents a constant wage model, with capital, labour and land as factors of production, which reproduces the historical tendencies and so can be used as a foundation for the various theories. The use of Chaplygins theorem in the proof of the main result also gives the paper a technical interest.

Primordial Perturbations in Einstein-Aether theories

El nostre objectiu es l'estudi d'extensions de la Relativitat General i, en particular, estem interessats en les teories que continguin camps vectorials addicionals. En aquests tipus de teories es necessari imposar que el vector ha de tenir norma fixa per evitar la presència d'un fantasma o grau de llibertat amb terme cinètic negatiu, i això implica que la simetria Lorentz està trencada espontàniament. El camp del aether només interactua gravitatòriament i la seva presència es difícil de detectar, no obstant això, durant inflació les fluctuacions del buit a escales petites d'un camp lleuger pot deixar una empremta en observables com les anisotropies del fons de radiació de microones. Les fluctuacions del Einstein-aether es comporten com els camps sense massa i això fa que inflació generi modes de longitud de ona llarga en els sectors escalar i vectorial. Hem estudiat la signatura del Einstein-aether dins l'espectre de pertorbacions primordials lluny del límit de de Sitter de inflació. Aquests modes escalars i vectorials poden deixar una empremta significativa en la radiació de fons de microones en funció dels paràmetres del model. Les observacions del fons de radiació de microones imposen restriccions fenomenològiques que redueixen els límits existents per aquesta classe de teoria. Amb aquest estudi del aether també esperem millorar el coneixement que tenim de una classe més ampla de teories que exhibeixen el mateix tipus de trencament de simetria.

A survey on recent p-adic integration theories and arithmetic applications

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

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.

Understanding the development of the ESDP: Perspectives and insights from historical institutionalism and theories of learning

How can we best understand the emergence of the European Security and Defence Policy (ESDP)? This paper applies the theories of historical institutionalism and experiential learning to offer a dynamic conceptualisation of moves towards an ESDP which highlights some of the causal factors that a more temporally-restricted analysis would miss. It firstly shows how the institutional and functional expansion of European Political Cooperation (EPC) over the course of the 1970s and 80s gave rise to a context in which the development of a security and defence dimension came to be viewed as more logical and even necessary. It then goes on to analyse some of the external factors (in the form of actors, events and institutions) that further pushed in this direction and proved to influence the policy’s subsequent evolution. The paper is therefore intended to act as a first-step to understanding the ESDP’s development from this perspective.

Three theories of liberalism for the three theories of federalism. A Hegelian turn

This paper links different political liberal theories, considered from the perspective of their moral ontology, with federal democracies. After giving a brief description of these theories, I discuss their relationship with the theoretical and institutional models of federalism. As methodological tools, the paper introduces some Hegel’s political concepts and deals with their potential application to the analysis of federalism, taken into account the case of minorities in multinational democracies. I postulate the need for a moral and institutional refinement of liberal-democratic patterns that is better able to accommodate national pluralism than has so far been achieved by traditional constitutionalism.

Social Security in Theory and Practice (II): Efficiency Theories, Narrative Theories, and Implications for Reform

166 countries have some kind of public old age pension. What economic forces create and sustain old age Social Security as a public program? Mulligan and Sala-i-Martin (1999b) document several of the internationally and historically common features of social security programs, and explore "political" theories of Social Security. This paper discusses the "efficiency theories", which view creation of the SS program as a full of partial solution to some market failure. Efficiency explanations of social security include the "SS as welfare for the elderly" the "retirement increases productivity to optimally manage human capital externalities", "optimal retirement insurance", the "prodigal father problem", the "misguided Keynesian", the "optimal longevity insurance", the "government economizing transaction costs", and the "return on human capital investment". We also analyze four "narrative" theories of social security: the "chain letter theory", the "lump of labor theory", the "monopoly capitalism theory", and the "Sub-but-Nearly-Optimal policy response to private pensions theory". The political and efficiency explanations are compared with the international and historical facts and used to derive implications for replacing the typical pay-as-you-go system with a forced savings plan. Most of the explanations suggest that forced savings does not increase welfare, and may decrease it.

Social security in theory and practice (II): Efficiency theories, narrative theories and implications for reform

166 countries have some kind of public old age pension. What economic forcescreate and sustain old age Social Security as a public program? Mulligan and Sala-i-Martin (1999b) document several of the internationally and historically common features of social security programs, and explore "political" theories of Social Security. This paper discusses the "efficiency theories", which view creation of the SS program as a full of partial solution to some market failure. Efficiency explanations of social security include the "SS as welfare for the elderly" the "retirement increases productivity to optimally manage human capital externalities", "optimal retirement insurance", the "prodigal father problem", the "misguided Keynesian", the "optimal longevity insurance", the "governmenteconomizing transaction costs", and the "return on human capital investment". We also analyze four "narrative" theories of social security: the "chain letter theory", the "lump of labor theory", the "monopoly capitalism theory", and the "Sub-but-Nearly-Optimal policy response to private pensions theory".The political and efficiency explanations are compared with the international and historical facts and used to derive implications for replacing the typical pay-as-you-go system with a forced savings plan. Most of the explanations suggest that forced savings does not increase welfare, and may decrease it.

Social security in theory and practice (I): Facts and political theories

166 countries have some kind of public old age pension. What economic forcescreate and sustain old age Social Security as a public program? We document some of the internationally and historically common features of Social Security programs including explicit and implicit taxes on labor supply, pay-as-you-go features, intergenerational redistribution, benefits which areincreasing functions of lifetime earnings and not means-tested. We partition theories of Social Security into three groups: "political", "efficiency" and "narrative" theories. We explore three political theories in this paper: the majority rational voting model (with its two versions: "the elderly as the leaders of a winning coalition with the poor" and the "once and for all election" model), the "time-intensive model of political competition" and the "taxpayer protection model". Each of the explanations is compared with the international and historical facts. A companion paper explores the "efficiency" and "narrative" theories, and derives implicationsof all the theories for replacing the typical pay-as-you-go system with a forced savings plan.