ERC FUNDED PROJECTS

The central research theme of this proposal is the study of social change (skills, productivity, attitudes and beliefs) in Europe along cohort lines and as a function of changing age composition. Using demographic methods, age-specific and cohort-specific changes shall be quantitatively disentangled. The impact of migration flows as well as fertility differentials combined with intergenerational transmissions will be taken into account. It is expected that viewed together, these analyses will result in significant new insights and represent frontier research about likely social and economic challenges associated with ageing and demographic change in Europe and the appropriate policies for coping with them. Unlike projections of long-term economic growth or energy use, demographic forecasts tend to have comparatively low margins of error, even for forecasts half a century ahead. Traits that change systematically along age or cohort lines may therefore be projected with some degree of accuracy, which in turn can allow governments and individuals to better foresee and improve policies for predictable social change. The study will investigate two major topics, the first relating to human capital, skills, and work performance; the second relating to beliefs and attitudes in Europe. Understanding age variation in productivity and how to improve senior workers skills and capacities are paramount for ageing countries. Moreover, individual-level demographic behaviour can have aggregate level implications, including changing societal values and belief structures. The binding element is how such projections will improve one s capacity to foresee and hence develop more targeted policies that relate to ageing societies.

981 415 €

Start date: 2009-10-01, End date: 2015-03-31

The collective behavior of quantum and classical many body systems such as ultracold atomic gases, nanowires, cuprates and micromagnets are currently subject of an intense experimental and theoretical research worldwide. Understanding the fascinating phenomena of Bose-Einstein condensation, Luttinger liquid vs non-Luttinger liquid behavior, high temperature superconductivity, and spontaneous formation of periodic patterns in magnetic systems, is an exciting challenge for theoreticians. Most of these phenomena are still far from being fully understood, even from a heuristic point of view. Unveiling the exotic properties of such systems by rigorous mathematical analysis is an important and difficult challenge for mathematical physics. In the last two decades, substantial progress has been made on various aspects of many-body theory, including Fermi liquids, Luttinger liquids, perturbed Ising models at criticality, bosonization, trapped Bose gases and spontaneous formation of periodic patterns. The techniques successfully employed in this field are diverse, and range from constructive renormalization group to functional variational estimates. In this research project we propose to investigate a number of statistical mechanics models by a combination of different mathematical methods. The objective is, on the one hand, to understand crossover phenomena, phase transitions and low-temperature states with broken symmetry, which are of interest in the theory of condensed matter and that we believe to be accessible to the currently available methods; on the other, to develop new techiques combining different and complementary methods, such as multiscale analysis and localization bounds, or reflection positivity and cluster expansion, which may be useful to further progress on important open problems, such as Bose-Einstein condensation, conformal invariance in non-integrable models, existence of magnetic or superconducting long range order.

650 000 €

Start date: 2010-01-01, End date: 2014-12-31

Reasoning, to derive conclusions from facts, is a fundamental task in Artificial Intelligence, arising in a wide range of applications from Robotics to Expert Systems. The aim of this project is to devise new efficient algorithms for real-world reasoning problems and to get new insights into the question of what makes a reasoning problem hard, and what makes it easy. As key to novel and groundbreaking results we propose to study reasoning problems within the framework of Parameterized Complexity, a new and rapidly emerging field of Algorithms and Complexity. Parameterized Complexity takes structural aspects of problem instances into account which are most significant for empirically observed problem-hardness. Most of the considered reasoning problems are intractable in general, but the real-world context of their origin provides structural information that can be made accessible to algorithms in form of parameters. This makes Parameterized Complexity an ideal setting for the analysis and efficient solution of these problems. A systematic study of the Parameterized Complexity of reasoning problems that covers theoretical and empirical aspects is so far outstanding. This proposal sets out to do exactly this and has therefore a great potential for groundbreaking new results. The proposed research aims at a significant impact on the research culture by setting the grounds for a closer cooperation between theorists and practitioners.

1 421 130 €

Start date: 2010-01-01, End date: 2014-12-31

A contact structure on an odd dimensional manifold in a maximally non integrable hyperplane field. It is the odd dimensional counterpart of a symplectic structure. Contact and symplectic topology is a recent and very active area that studies intrinsic questions about existence, (non) uniqueness and rigidity of contact and symplectic structures. It is intimately related to many other important disciplines, such as dynamical systems, singularity theory, knot theory, Morse theory, complex analysis, ... Legendrian submanifolds are a distinguished class of submanifolds in a contact manifold, which are tangent to the contact distribution. These manifolds are of a particular interest in contact topology. Important classes of Legendrian submanifolds can be described using generating families, and this description can be used to define Legendrian invariants via Morse theory. Other the other hand, Legendrian contact homology is an invariant for Legendrian submanifolds, based on holomorphic curves. The goal of this research proposal is to study the relationship between these two approaches. More precisely, we plan to show that the generating family homology and the linearized Legendrian contact homology can be defined for the same class of Legendrian submanifolds, and are isomorphic. This correspondence should be established using a parametrized version of symplectic homology, being developed by the Principal Investigator in collaboration with Oancea. Such a result would give an entirely new type of information about holomorphic curves invariants. Moreover, it can be used to obtain more general structural results on linearized Legendrian contact homology, to extend recent results on existence of Reeb chords, and to gain a much better understanding of the geography of Legendrian submanifolds.

710 000 €

Start date: 2009-11-01, End date: 2014-10-31