Hilbert Functions of Filtered Modules

In this presentation we shall deal with some aspects of the theory of Hilbert functions of modules over local rings, and we intend to guide the reader along one of the possible routes through the last three decades of progress in this area of dynamic mathematical activity. Motivated by the ever increasing interest in this field, our goal is to gather together many new developments of this theory into one place, and to present them using a unifying approach which gives self-contained and easier proofs. In this text we shall discuss many results by different authors, following essentially the direction typified by the pioneering work of J. Sally. Our personal view of the subject is most visibly expressed by the presentation of Chapters 1 and 2 in which we discuss the use of the superficial elements and related devices. Basic techniques will be stressed with the aim of reproving recent results by using a more elementary approach. Over the past few years several papers have appeared which extend classical results on the theory of Hilbert functions to the case of filtered modules. The extension of the theory to the case of general filtrations on a module has one more important motivation. Namely, we have interesting applications to the study of graded algebras which are not associated to a filtration, in particular the Fiber cone and the Sally-module. We show here that each of these algebras fits into certain short exact sequences, together with algebras associated to filtrations. Hence one can study the Hilbert function and the depth of these algebras with the aid of the know-how we got in the case of a filtration.Comment: 127 pages, revised version. Comments and remarks are welcom

Bank liquidity and financial stability.

Fluctuations in investor risk aversion are often cited as a factor explaining crises on financial markets. The alternation between periods of bullishness prompting investors to make risky investments, and periods of bearishness, when they retreat to the safest forms of investments, could be at the root of sharp fluctuations in asset prices. One problem in the assessment of these different periods is clearly distinguishing the risk perceived by agents from risk aversion itself. There are several types of risk aversion indicators used by financial institutions (the VIX, the LCVI, the GRAI, etc.). These indices, which are estimated in diverse ways, often show differing developments, although it is not possible to directly assess which is the most accurate. An interesting method in this respect is to link the indicators to financial crises. In principle, financial crises should coincide with periods in which risk aversion increases. Here we estimate probabilities of financial crises –currency and stock market crises– using the different risk aversion indicators as explanatory variables. This allows us to assess their respective predictive powers. The tests carried out show that risk aversion does tend to increase before crises, at least when it is measured by the most relevant indices. This variable is a good leading indicator of stock market crises, but is less so for currency crises.

How Climate, Uplift and Erosion Shaped the Alpine Topography

Decades of scientific research on the European Alps have helped quantify the vast array of processes that shape the Earth’s surface. Patterns in rock exhumation, surface erosion and topographic changes can be compared to sediment yields preserved in sedimentary basins or collected from modern rivers. Erosion-driven isostatic uplift explains up to ~50% of the modern geodetic rock uplift rates; the remaining uplift reveals the importance of internal processes (tectonics, deep-seated geodynamics) and external processes (glacial rebound, topographic changes). We highlight recent methodological and conceptual developments that have contributed to our present view of the European Alps, and we provide suggestions on how to fill the gaps in our understanding

Preliminary hidrological results from Sarennes glacier basin, French Alps

Located in the French Alps, Glacier de Sarennes is a small glacier which has its mass balance, measured since 1948. Now since 1992, the Snow Engineenng and Avalanche control department of Cemagref Grenoble measures water leve1 in the emissary of this glacier at the altitude of 2800 meters. The time step of these records is 10 minutes. The aim of this study is to realize the first hydrological assessment, despite having few records until now, to be able to control the new experimental discharge station, and to extract the first scientific results

Renormalization of spectral lineshape and dispersion below Tc in Bi2Sr2CaCu2O8+d

Angle-resolved photoemission (ARPES) data in the superconducting state of Bi2Sr2CaCu2O8+d show a kink in the dispersion along the zone diagonal, which is related via a Kramers-Kronig analysis to a drop in the low-energy scattering rate. As one moves towards (pi,0), this kink evolves into a spectral dip. The occurrence of these anomalies in the dispersion and lineshape throughout the zone indicate the presence of a new energy scale in the superconducting state.Comment: New Figure 3 with expanded discussio

Application of the scattering rate sum-rule to the interplane optical conductivity of high temperature superconductors: pseudogap and bi-layer effects

We use a recently proposed model of the interplane conductivity of high temperature superconductors to investigate the `scattering rate sum-rule' introduced by Basov and co-workers. We present a new derivation of the sum-rule. The quantal and thermal fluctuations of the order parameter which have been argued to produce the observed pseudogap behavior are shown to increase the total integrated `scattering rate' but may either increase or decrease the `quasiparticle' contribution from frequencies greater than twice the superconducting gap.Comment: 4 pages, 5 figures, revise

Charge order, metallic behavior and superconductivity in La_{2-x}Ba_xCuO_4 with x=1/8

The ab-plane optical properties of a cleaved single crystal of La_{2-x}Ba_xCuO_4 for x=1/8 (T_c ~ 2.4 K) have been measured over a wide frequency and temperature range. The low-frequency conductivity is Drude-like and shows a metallic response with decreasing temperature. However, below ~ 60 K, corresponding to the onset of charge-stripe order, there is a rapid loss of spectral weight below about 40 meV. The gapping of single-particle excitations looks surprisingly similar to that observed in superconducting La_{2-x}Sr_{x}CuO_4, including the presence of a residual Drude peak with reduced weight; the main difference is that the lost spectral weight moves to high, rather than zero, frequency, reflecting the absence of a bulk superconducting condensate.Comment: 4 pages, with 1 table and 3 figure