ERC FUNDED PROJECTS

Topological materials have developed rapidly in recent years, with my previous ERC-AG project 3-TOP playing a major role in this development. While so far no bulk topological superconductor has been unambiguously demonstrated, their properties can be studied in a very flexible manner by inducing superconductivity through the proximity effect into the surface or edge states of a topological insulator. In 4-TOPS we will explore the possibilities of this approach in full, and conduct a thorough study of induced superconductivity in both two and three dimensional HgTe based topological insulators. The 4 avenues we will follow are: -SQUID based devices to investigate full phase dependent spectroscopy of the gapless Andreev bound state by studying their Josephson radiation and current-phase relationships. -Experiments aimed at providing unambiguous proof of localized Majorana states in TI junctions by studying tunnelling transport into such states. -Attempts to induce superconductivity in Quantum Hall states with the aim of creating a chiral topological superconductor. These chiral superconductors host Majorana fermions at their edges, which, at least in the case of a single QH edge mode, follow non-Abelian statistics and are therefore promising for explorations in topological quantum computing. -Studies of induced superconductivity in Weyl semimetals, a completely unexplored state of matter. Taken together, these four sets of experiments will greatly enhance our understanding of topological superconductivity, which is not only a subject of great academic interest as it constitutes the study of new phases of matter, but also has potential application in the field of quantum information processing.

2 497 567 €

Start date: 2017-06-01, End date: 2022-05-31

Although we have extensive knowledge of many important processes in cell biology, including information on many of the molecules involved and the physical interactions among them, we still do not understand most of the dynamical features that are the essence of living systems. This is particularly true for the actin cytoskeleton, a major component of the internal architecture of eukaryotic cells. In living cells, actin networks constantly assemble and disassemble filaments while maintaining an apparent stable structure, suggesting a perfect balance between the two processes. Such behaviors are called “dynamic steady states”. They confer upon actin networks a high degree of plasticity allowing them to adapt in response to external changes and enable cells to adjust to their environments. Despite their fundamental importance in the regulation of cell physiology, the basic mechanisms that control the coordinated dynamics of co-existing actin networks are poorly understood. In the AAA project, first, we will characterize the parameters that allow the coupling among co-existing actin networks at steady state. In vitro reconstituted systems will be used to control the actin nucleation patterns, the closed volume of the reaction chamber and the physical interaction of the networks. We hope to unravel the mechanism allowing the global coherence of a dynamic actin cytoskeleton. Second, we will use our unique capacity to perform dynamic micropatterning, to add or remove actin nucleation sites in real time, in order to investigate the ability of dynamic networks to adapt to changes and the role of coupled network dynamics in this emergent property. In this part, in vitro experiments will be complemented by the analysis of actin network remodeling in living cells. In the end, our project will provide a comprehensive understanding of how the adaptive response of the cytoskeleton derives from the complex interplay between its biochemical, structural and mechanical properties.

2 349 898 €

Start date: 2017-09-01, End date: 2022-08-31

The understanding of spatial, social and dynamical organization of large numbers of agents is presently a fundamental issue in modern science. ADORA focuses on problems motivated by biology because, more than anywhere else, access to precise and many data has opened the route to novel and complex biomathematical models. The problems we address are written in terms of nonlinear partial differential equations. The flux-limited Keller-Segel system, the integrate-and-fire Fokker-Planck equation, kinetic equations with internal state, nonlocal parabolic equations and constrained Hamilton-Jacobi equations are among examples of the equations under investigation. The role of mathematics is not only to understand the analytical structure of these new problems, but it is also to explain the qualitative behavior of solutions and to quantify their properties. The challenge arises here because these goals should be achieved through a hierarchy of scales. Indeed, the problems under consideration share the common feature that the large scale behavior cannot be understood precisely without access to a hierarchy of finer scales, down to the individual behavior and sometimes its molecular determinants. Major difficulties arise because the numerous scales present in these equations have to be discovered and singularities appear in the asymptotic process which yields deep compactness obstructions. Our vision is that the complexity inherent to models of biology can be enlightened by mathematical analysis and a classification of the possible asymptotic regimes. However an enormous effort is needed to uncover the equations intimate mathematical structures, and bring them at the level of conceptual understanding they deserve being given the applications motivating these questions which range from medical science or neuroscience to cell biology.

2 192 500 €

Start date: 2017-09-01, End date: 2023-02-28

Parameterized mathematical models have been central to the understanding and design of communication, networking, and radar systems. However, they often lack the ability to model intricate interactions innate in complex systems. On the other hand, data-driven approaches do not need explicit mathematical models for data generation and have a wider applicability at the cost of flexibility. These approaches need labelled data, representing all the facets of the system interaction with the environment. With the aforementioned systems becoming increasingly complex with intricate interactions and operating in dynamic environments, the number of system configurations can be rather large leading to paucity of labelled data. Thus there are emerging networks of systems of critical importance whose cognition is not effectively covered by traditional approaches. AGNOSTIC uses the process of exploration through system probing and exploitation of observed data in an iterative manner drawing upon traditional model-based approaches and data-driven discriminative learning to enhance functionality, performance, and robustness through the notion of active cognition. AGNOSTIC clearly departs from a passive assimilation of data and aims to formalize the exploitation/exploration framework in dynamic environments. The development of this framework in three applications areas is central to AGNOSTIC. The project aims to provide active cognition in radar to learn the environment and other active systems to ensure situational awareness and coexistence; to apply active probing in radio access networks to infer network behaviour towards spectrum sharing and self-configuration; and to learn and adapt to user demand for content distribution in caching networks, drastically improving network efficiency. Although these cognitive systems interact with the environment in very different ways, sufficient abstraction allows cross-fertilization of insights and approaches motivating their joint treatment.

2 499 595 €

Start date: 2017-10-01, End date: 2022-09-30