ERC FUNDED PROJECTS

The purpose of this project is to develop new methods for solving boundary value problems (BVPs) for nonlinear integrable partial differential equations (PDEs). Integrable PDEs can be analyzed by means of the Inverse Scattering Transform, whose introduction was one of the most important developments in the theory of nonlinear PDEs in the 20th century. Until the 1990s the inverse scattering methodology was pursued almost entirely for pure initial-value problems. However, in many laboratory and field situations, the solution is generated by what corresponds to the imposition of boundary conditions rather than initial conditions. Thus, an understanding of BVPs is crucial. In an exciting sequence of events taking place in the last two decades, new tools have become available to deal with BVPs for integrable PDEs. Although some important issues have already been resolved, several major problems remain open. The aim of this project is to solve a number of these open problems and to find solutions of BVPs which were heretofore not solvable. More precisely, the proposal has eight objectives: 1. Develop methods for solving problems with time-periodic boundary conditions. 2. Answer some long-standing open questions raised by series of wave-tank experiments 35 years ago. 3. Develop a new approach for the study of space-periodic solutions. 4. Develop new approaches for the analysis of BVPs for equations with 3 x 3-matrix Lax pairs. 5. Derive new asymptotic formulas by using a nonlinear version of the steepest descent method. 6. Construct disk and disk/black-hole solutions of the stationary axisymmetric Einstein equations. 7. Solve a BVP in Einstein's theory of relativity describing two colliding gravitational waves. 8. Extend the above methods to BVPs in higher dimensions.

2 000 000 €

Start date: 2016-05-01, End date: 2021-04-30

Title: Discrete and convex geometry: challenges, methods, applications Abstract: Research in discrete and convex geometry, using tools from combinatorics, algebraic topology, probability theory, number theory, and algebra, with applications in theoretical computer science, integer programming, and operations research. Algorithmic aspects are emphasized and often serve as motivation or simply dictate the questions. The proposed problems can be grouped into three main areas: (1) Geometric transversal, selection, and incidence problems, including algorithmic complexity of Tverberg's theorem, weak epsilon-nets, the k-set problem, and algebraic approaches to the Erdos unit distance problem. (2) Topological methods and questions, in particular topological Tverberg-type theorems, algorithmic complexity of the existence of equivariant maps, mass partition problems, and the generalized HeX lemma for the k-coloured d-dimensional grid. (3) Lattice polytopes and random polytopes, including Arnold's question on the number of convex lattice polytopes, limit shapes of lattice polytopes in dimension 3 and higher, comparison of random polytopes and lattice polytopes, the integer convex hull and its randomized version.

1 298 012 €

Start date: 2011-04-01, End date: 2017-03-31

This project will open up new horizons in the study of emotional learning by describing and modeling its role in social interaction. It brings together a novel set of experimental manipulations with two hitherto unconnected lines of research; biology of aversive learning and social cognition, with the aim to answer four specific objectives, namely to identify the mechanisms of aversive learning (1) about others and its dependence on stimulus bound (e.g. ethnic group belonging) and conceptual (e.g. moral and social status) features; (2) from others through observation, and its dependence on processing of stimulus bound (e.g. emotional expressiveness) and conceptual (e.g. empathy and mental state attributions) features; (3) during interaction and its dependence social characteristics as described in 1 and 2; and (4) build and test a neural model of social-emotional learning. To achieve these objectives, this project proposes a multi-method research program using novel behavioral experimental paradigms and manipulated virtual environments, drawing on cognitive neuroscience, psychophysiology, and behavioral genetics. It is predicted that social emotional learning will be accomplished through the interaction of four, partially overlapping, neural networks coding for affective, associative, social cognitive and instrumental/goal directed aspects, respectively. Whereas it is expected that the two first networks will be common to classical conditioning and social learning, the latter is hypothesized to be distinguished by its reliance on the social-cognitive network. The fourth network is predicted to be integral to the social learning through interactions and the shaping of behavioral norms. The proposed research will enhance our understanding of important social phenomena, such as the emergence and maintanance of group conflicts and norm compliance. It will also shed light on common psychological disorders, such as social anxiety, autism and psychopathy that are characterized by dysfunctions of the social emotional learning system.

1 498 244 €

Start date: 2012-12-01, End date: 2018-11-30

Metabolic engineering is the development of new cell factories or improving existing ones, and it is the enabling science that allows for sustainable production of fuels and chemicals through biotechnology. With the development in genomics and functional genomics, it has become interesting to evaluate how advanced high-throughput experimental techniques (transcriptome, proteome, metabolome and fluxome) can be applied for improving the process of metabolic engineering. These techniques have mainly found applications in life sciences and studies of human health, and it is necessary to develop novel bioinformatics techniques and modelling concepts before they can provide physiological information that can be used to guide metabolic engineering strategies. In particular it is challenging how these techniques can be used to advance the use of mathematical modelling for description of the operation of complex metabolic networks. The availability of robust mathematical models will allow a wider use of mathematical models to drive metabolic engineering, in analogy with other fields of engineering where mathematical modelling is central in the design phase. In this project the advancement of novel concepts, models and technologies for enhancing metabolic engineering will be done in connection with the development of novel cell factories for high-level production of different classes of products. The chemicals considered will involve both commodity type chemicals like 3-hydroxypropionic acid and malic acid, that can be used for sustainable production of polymers, an industrial enzyme and pharmaceutical proteins like human insulin.

2 499 590 €

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