Why do we have to connect natural disasters history, natural hazards history and environmental history? One can think that these objects are very close. But the international state of the art proves that's not true. Natural disasters look apart when researchers don't want to write an anthropocentric history. The same one can use natural disasters to prove how important it is to study environmental history. Furthermore, XXth century specialists used to deal with risks, accident, crisis whereas disasters are more connected with old times. This research project doesn't aim to study disasters for themselves. The idea is more to connect three topics that don't look each other (disasters, risk, and environment). Natural disasters have rarely been the object focused upon entirely by historians, but rather a historiographic junction, a meeting point for the fascination this type of event inspires, demographic history and the history of fear and of mentalities. The multiplication of conferences and works dedicated to this theme over the last ten years seems to suggest that this time has past. These works respond to an ever strengthening social demand, fed by the apparition of new risks and tragic events, the discovery of an unsuspected vulnerability, acute controversies over strategic concepts (responsibility, prevention, precaution). However, this new field of research is still in midstream. Monographs of disasters dominate; few works have risked the study of the process, the evolution over the long-term. If a certain number of events were to be analysed in detail, other competing models reappear at the slightest move towards generality. The first, often implicit, rests on the distinction between societies of natural disasters and societies at risk, that is to say a certain way of defining modernity from the 19th century by the will to liberate oneself of the dangers of nature, thanks to the system of science and production. The current debate around risk is fed by bringing into question this paradigm since Ulrich Beck and Anthony Giddens showed that post-modern societies are characterised by the proliferation of all natural risks and of globalized threats produced by societies themselves. In sum, a new paradigm which wavered between, on the one hand, a brutal return to the middle ages of disasters and fears, and on the other hand, a new less predictable modernity which was turned towards the future. The second model, which supports the first, is that of a linear history of the relationship between man and nature, an occidental conception of historic destiny as the confrontation between two orders of reality. For the modern era, this linearity takes the form of progressive secularization of disaster, passing from divine anger to natural phenomena. At the same time, the implementation of state machinery with an increasing hold over the kingdom accompanied the project to master Nature and to insulate themselves against its blows. To examine these schemas, we must first understand the way of writing a history of natural disasters and resolve several problems. Historians often remain confined, by natural sciences, to the role of archive specialist, or of supplier of data to be interpreted by hazard specialists. The importing of concepts formed by sociology, political science and geography do not succeed at hiding the division between natural and social perspectives. The tenants of the fact itself exist independently of man and often come up against the tenants of cultural fact.

In this proposal, we aim to explore several aspects of the genetic and environmental (non-genetic) risk factors of cerebrovascular disease. The first two parts of the proposal focus on genetic (Task 1) and environmental (Task 2) risk factors of covert MRI-defined cerebrovascular disease (MRI-CVD) and the interaction between both. We will be using a competitive genome-wide approach for Task 1 and various standardized risk factor measurements including sophisticated structural and functional vascular endophenotypes in Task 2. The third part of the proposal aims at exploring the link between covert MRI-CVD and cognitive decline and to assess whether genetic susceptibility factors to MRI-CVD are also associated with an increased risk of cognitive decline (Task 3). This will be performed within the ongoing 3C Study and the EVA Study, 2 large prospective cohort studies on French community-based participants. In Task 1 our goal is to identify genetic risk factors of MRI-defined cerebrovascular disease (MRI-CVD) in community-dwelling older persons. We plan to perform three genome-wide association studies on the following phenotypes: (i) white matter hyperintensity (WMH) volume; (ii) GWAS of WMH progression; (iii) extensive MRI-CVD (defined by the presence of at least one covert MRI-defined brain infarct [CBI] and / or WMH volume in the top quartile of the distribution). For all these analyses the discovery cohort will be the 3C-Dijon MRI Study (N=1,746 for cross-sectional analyses and N=1,298 for longitudinal analyses, mean age = 72.4 years). For the GWAS on WMH volume and on extensive MRI-CVD the replication cohort will be the EVA-MRI Study (N=758, mean age = 68.9 years). For the GWAS on WMH progression no longitudinal MRI data is available in the EVA study, we are planning an in silico replication and meta-analysis within the CHARGE consortium, including several large population-based studies with brain MRI and genome-wide data (Cohorts for Heart and Aging Research in Genomic Epidemiology - www.chargeconsortium.com). The neurological working group within this consortium is currently working on a GWAS meta-analysis project of WMH progression (letter attached). In Task 2 we aim to explore environmental (non-genetic) risk factors for WMH volume progression, as well as the interaction of these with genetic risk factors. In the first two subprojects we plan to explore the relationship of vascular stroke risk factors and associated biomarkers with WMH progression and to assess whether subclinical markers of atherosclerosis in cervical and peripheral arteries are associated with an increased risk of WMH progression. In the third subproject we intend to explore interactions between genetic susceptibility factors and hypertension (one of the most powerful risk factors of WMH known so far) on the association with WMH volume. The analyses will be performed in the 3C-Dijon MRI Study, with a replication analysis in the EVA-MRI Study for the third subproject. In Task 3 we plan to explore the association of MRI-CVD with clinical events and test whether genetic risk factors of MRI-CVD are also associated with an increased risk of these clinical events. In a first part we will explore the differential association of CBI and WMH volume with the risk of dementia and evaluate the association of WMH volume and WMH progression with cognitive decline. This will be performed in the 3C-Dijon MRI Study, after exclusion of participants with dementia and a history of stroke at baseline. In a second part we will test the association with cognitive decline of genetic variants found to be associated with MRI-CVD. This will be performed in the 3C Study participants with good quality DNA and at least 2 neuropsychological assessments available, with a replication analysis of significant association in the EVA study.

The recent succes of collision attacks on cryptographic hash functions have created some turmoil in the cryptologic research community. In particular, collisions for MD5 and SHA-0 have been exhibited, and some costly but feasible attacks on SHA-1 have been described. This represent a potential threat for some cryptographic applications, as digital signatures. We propose two main topics for our project. 1) Understand the best attacks, in particular those presented by the Chinese researcher Wang. Actually, she provides some equations that allow the construction of collisions. It is possible to check the validity of those equations, but the way they are obtained is not very clear and deserves to be carefully examined and may hopefully help to define design criteria. 2) Find new design techniques for secure hash functions. In particular, we propose to extend some recent works on hash functions with security reduction. By combining those functions using constructions `a la Merkle-Damgard, we hope to produce fast cryptographic hash functions with a proof of security.

This project lies in the area of arithmetic and algebraic geometry. It aims at advancing both arithmetic and geometric aspects of $p$-adic Hodge theory by focusing on two of the deepest and most challenging questions : the $p$-adic Langlands programme for the arithmetic side and the $p$-adic Simpson correspondence for the geometric side. The $p$-adic Langlands programme was born at the turn of the 21th century with the aim of understanding how the $p$-adic Hodge theory on the Galois representations side could be understood on the $GL_n$ representations side (it is indeed essentially absent from the classical Langlands programme). More precisely, the point is to understand the $p$-adic representations of $GL_n$ of a finite extension of $Q_p$ that are realized on the completed $p$-adic étale cohomology of a tower of Shimura varieties. One expects these $p$-adic representations of $GL_n$ at least to "contain" the Fontaine's theory of the $p$-adic local Galois representations associated to those algebraic automorphic representations that are related to the relevant Shimura varieties. This $p$-adic programme is still in a first development phase (it is essentially complete only for $GL_2(Q_p)$), yet it has already produced deep applications to modularity theorems. Our aim is to develop it and generalize it, in particular to state (possibly conjectural) results that outweigh the current ones. The $p$-adic Simpson correspondence, recently initiated by Faltings, aims at describing all $p$-adic representations of the fundamental group of a (proper) smooth variety over a $p$-adic field in terms of linear algebra (Higgs modules). While the theory is still in an early development stage, it already appears as an important theoretical headway, with many deep potential applications both in arithmetics and in geometry ($p$-adic Galois representations, the cohomology of Shimura varieties, p-adic uniformization,...). Our project aims at developing the $p$-adic correspondence on the model of the complex Simpson theory from which it is inspired. Our main goals are in particular to extend its range of applications and to describe as precisely as possible its image (which corresponds to the difficult part of Simpson's results in the complex case).

The aim of this project is to tackle mathematical issues that are relevant for problems at the core of international interest in physics, and for which several Nobel prizes have been awarded: the Quantum Hall effect in Bose Einstein condensates. For that purpose, - our group is made up of two teams, one of mathematicians and one of physicists. - - The physics of quantized vortices is of tremendous importance in the field of quantum fluids and extends beyond condensed matter physics. Indeed, rearrangements of a vortex lattice in the interior of neutron stars have been proposed as an explanation of the so-called glitches in the rotation - frequency of pulsars. The cosmic strings are topological line defects of cosmological extent akin to the vortices of liquid Helium and their role in galaxy formation is the subject of present research in cosmology. Ultracold gaseous Bose-Einstein condensates - allow tests in the laboratory to study various aspects of - macroscopic quantum physics. - In particular, the quest - for vortices has been immediate. - The possibility of tuning many parameters of the system through - atomic physics techniques turns these gaseous systems into extremely - attractive objects. - - The atoms are confined in a potential created by an external - magnetic field and/or a superposition of laser beams, which gives - access to many different geometries. To nucleate vortices, one has - to add a certain amount of angular momentum to the gas. This can be - done by rotation. In - 2000, the ENS team of Jean Dalibard at Laboratoire - Kastler-Brossel succeeded in observing vortices in a single - component condensate, followed by teams at the MIT and Oxford. This - has triggered off many mathematical works on vortices and the - Abrikosov vortex lattice. All these experimental situations are described by a mean-field approach, where the system - is characterized by a macroscopic wave function solving the - Gross-Pitaevskii or nonlinear Schrodinger equation. - The mathematical tools involve PDE's, energy estimates, homogeneisation, - analysis of the spectrum of some operator, and more recently semi-classical analysis - and the introduction of Bargmann spaces. Our interest in this project - is still in the vortex lattice, but in a situation where - the mean field model is no longer valid because the states are - highly correlated, similarly to the fractional quantum Hall states - of electrons in two-dimensional structures. Thus, one has to - consider the quantum $N$ body hamiltonian. - - Current physical interest is now for a rapid rotation regime: the - rotation frequency becomes close to the transverse trapping - frequency. The centrifugal and trapping forces then nearly - compensate each other and the spatial extent of the condensate - becomes very large. This is a most interesting regime since it is - equivalent to the situation leading to the quantum Hall effect in - two-dimensional electron gases. Depending on the ratio between the - number of vortices and the number of particles, the ground state of - the system will be well approximated by a macroscopic wave function - or it will be a strongly correlated state. The former case is the - one - that we have started to study but that still leads to very - interesting open questions, in particular on the study of the - Abrikosov lattice, as well as the behaviour of the lattice - (melting) as a function of temperature. The case of strongly - correlated states is even more fascinating as it is directly - connected to the physics of fractional Quantum Hall phenomena. This - regime has not yet been reached experimentally. It is the core of - our project and requires the analysis of the quantum $N$ body - hamiltonian for bosons. The issues that we want to understand are new and open - mathematically. Indeed, all the mathematical works - on the thermodynamical limit lead to situations where the - asymptotic problem is de-correlated and thus the methods cannot be - used as such. Our problems display links w...