ERC FUNDED PROJECTS

The goal of this proposal is to fundamentally change the way we build and reason about software. We aim to develop new kinds of statistical programming systems that provide probabilistically likely solutions to tasks that are difficult or impossible to solve with traditional approaches. These statistical programming systems will be based on probabilistic models of massive codebases (also known as ``Big Code'') built via a combination of advanced programming languages and powerful machine learning and natural language processing techniques. To solve a particular challenge, a statistical programming system will query a probabilistic model, compute the most likely predictions, and present those to the developer. Based on probabilistic models of ``Big Code'', we propose to investigate new statistical techniques in the context of three fundamental research directions: i) statistical program synthesis where we develop techniques that automatically synthesize and predict new programs, ii) statistical prediction of program properties where we develop new techniques that can predict important facts (e.g., types) about programs, and iii) statistical translation of programs where we investigate new techniques for statistical translation of programs (e.g., from one programming language to another, or to a natural language). We believe the research direction outlined in this interdisciplinary proposal opens a new and exciting area of computer science. This area will combine sophisticated statistical learning and advanced programming language techniques for building the next-generation statistical programming systems. We expect the results of this proposal to have an immediate impact upon millions of developers worldwide, triggering a paradigm shift in the way tomorrow's software is built, as well as a long-lasting impact on scientific fields such as machine learning, natural language processing, programming languages and software engineering.

1 500 000 €

Start date: 2016-04-01, End date: 2021-03-31

"The urgent need to develop inexpensive and ubiquitous solar energy conversion cannot be overstated. Solution processed organic semiconductors can enable this goal as they support drastically less expensive fabrication techniques compared to traditional semiconductors. Molecular organic semiconductors (MOSs) offer many advantages to their more-common pi-conjugated polymer counterparts, however a clear and fundamental challenge to enable the goal of high performance solution-processable molecular organic semiconductor devices is to develop the ability to control the crystal packing, crystalline domain size, and mixing ability (for multicomponent blends) in the thin-film device geometry. The CEMOS project will accomplish this by pioneering innovative methods of “bottom-up” crystal engineering for organic semiconductors. We will employ specifically tailored molecules designed to leverage both thermodynamic and kinetic aspects of molecular organic semiconductor systems to direct and control crystalline packing, promote crystallite nucleation, compatibilize disparate phases, and plasticize inelastic materials. We will demonstrate that our new classes of materials can enable the tuning of the charge carrier transport and morphology in MOS thin films, and we will evaluate their performance in actual thin-film transistor (TFT) and organic photovoltaic (OPV) devices. Our highly interdisciplinary approach, combining material synthesis and device fabrication/evaluation, will not only lead to improvements in the performance and stability of OPVs and TFTs but will also give deep insights into how the crystalline packing—independent from the molecular structure—affects the optoelectronic properties. The success of CEMOS will rapidly advance the performance of MOS devices by enabling reproducible and tuneable performance comparable to traditional semiconductors—but at radically lower processing costs."

1 477 472 €

Start date: 2014-01-01, End date: 2018-12-31

The ComplexData project aims at advancing our understanding of the statistical treatment of varied types of complex data by generating new theory and methods, and to obtain progress in concrete current biophysical problems through the implementation of the new tools developed. Complex Data constitute data where the basic object of observation cannot be described in the standard Euclidean context of statistics, but rather needs to be thought of as an element of an abstract mathematical space with special properties. Scientific progress has, in recent years, begun to generate an increasing number of new and complex types of data that require statistical understanding and analysis. Four such types of data that are arising in the context of current scientific research and that the project will be focusing on are: random integral transforms, random unlabelled shapes, random flows of functions, and random tensor fields. In these unconventional contexts for statistics, the strategy of the project will be to carefully exploit the special aspects involved due to geometry, dimension and randomness in order to be able to either adapt and synthesize existing statistical methods, or to generate new statistical ideas altogether. However, the project will not restrict itself to merely studying the theoretical aspects of complex data, but will be truly interdisciplinary. The connecting thread among all the above data types is that their study is motivated by, and will be applied to concrete practical problems arising in the study of biological structure, dynamics, and function: biophysics. For this reason, the programme will be in interaction with local and international contacts from this field. In particular, the theoretical/methodological output of the four programme research foci will be applied to gain insights in the following corresponding four application areas: electron microscopy, protein homology, DNA molecular dynamics, brain imaging.

681 146 €

Start date: 2011-06-01, End date: 2016-05-31

The developments of Statistical Mechanics and Quantum Field Theory are among the major achievements of the 20th century's science. During the second half of the century, these two subjects started to converge. In two dimensions, this resulted in a most remarkable chapter of mathematical physics: Conformal Field Theory (CFT) reveals deep structures allowing for extremely precise investigations, making such theories powerful building blocks of many subjects of mathematics and physics. Unfortunately, this convergence has remained non-rigorous, leaving most of the spectacular field-theoretic applications to Statistical Mechanics conjectural. About 15 years ago, several mathematical breakthroughs shed new light on this picture. The development of SLE curves and discrete complex analysis has enabled one to connect various statistical mechanics models with conformally symmetric processes. Recently, major progress was made on a key statistical mechanics model, the Ising model: the connection with SLE was established, and many formulae predicted by CFT were proven. Important advances towards connecting Statistical Mechanics and CFT now appear possible. This is the goal of this proposal, which is organized in three objectives: (I) Build a deep correspondence between the Ising model and CFT: reveal clear links between the objects and structures arising in the Ising and CFT frameworks. (II) Gather the insights of (I) to study new connections to CFT, particularly for minimal models, current algebras and parafermions. (III) Combine (I) and (II) to go beyond conformal symmetry: link the Ising model with massive integrable field theories. The aim is to build one of the first rigorous bridges between Statistical Mechanics and CFT. It will help to close the gap between physical derivations and mathematical theorems. By linking the deep structures of CFT to concrete models that are applicable in many subjects, it will be potentially useful to theoretical and applied scientists.

998 005 €

Start date: 2017-03-01, End date: 2022-02-28

The analysis and synthesis of complex 3D geometric data sets is of crucial importance in many scientific disciplines (e.g. bio-medicine, material science, mechanical engineering, physics) and industrial applications (e.g. drug design, entertainment, architecture). We are currently witnessing a tremendous increase in the size and complexity of geometric data, largely fueled by significant advances in 3D acquisition and digital production technology. However, existing computational tools are often not suited to handle this complexity. The goal of this project is to explore a fundamentally different way of processing 3D geometry. We will investigate a new generalized model of geometric symmetry as a unifying concept for studying spatial organization in geometric data. This model allows exposing the inherent redundancies in digital 3D data and will enable truly scalable algorithms for analysis, processing, and design of large-scale geometric data sets. The proposed research will address a number of fundamental questions: What is the information content of 3D geometric models? How can we represent, store, and transmit geometric data most efficiently? Can we we use symmetry to repair deficiencies and reduce noise in acquired data? What is the role of symmetry in the design process and how can it be used to reduce complexity? I will investigate these questions with an integrated approach that combines thorough theoretical studies with practical solutions for real-world applications. The proposed research has a strong interdisciplinary component and will consider the same fundamental questions from different perspectives, closely interacting with scientists of various disciplines, as well artists, architects, and designers.

1 160 302 €

Start date: 2011-02-01, End date: 2016-01-31

"Strongly correlated materials exhibit some of the most remarkable phenonomena found in condensed matter systems. They typically involve many active degrees of freedom (spin, charge, orbital), which leads to numerous competing states and complicated phase diagrams. A new perspective on correlated many-body systems is provided by the nonequilibrium dynamics, which is being explored in transport studies on nanostructures, pump-probe experiments on correlated solids, and in quench experiments on ultra-cold atomic gases. An advanced theoretical framework for the study of correlated lattice models, which can be adapted to nonequilibrium situations, is dynamical mean field theory (DMFT). One aim of this proposal is to develop ""nonequilibrium DMFT"" into a powerful tool for the simulation of excitation and relaxation processes in interacting many-body systems. The big challenge in these simulations is the calculation of the real-time evolution of a quantum impurity model. Recently developed real-time impurity solvers have, however, opened the door to a wide range of applications. We will improve the efficiency and flexibility of these methods and develop complementary approaches, which will extend the accessible parameter regimes. This machinery will be used to study correlated lattice models under nonequilibrium conditions. The ultimate goal is to explore and qualitatively understand the nonequilibrium properties of ""real"" materials with active spin, charge, orbital and lattice degrees of freedom. The ability to simulate the real-time dynamics of correlated many-body systems will be crucial for the interpretation of experiments and the discovery of correlation effects which manifest themselves only in the form of transient states. A proper understanding of the most basic nonequilibrium phenomena in correlated solids will help guide future experiments and hopefully lead to new technological applications such as ultra-fast switches or storage devices."

1 493 178 €

Start date: 2012-02-01, End date: 2017-01-31

One of the oldest and most important questions in PDE theory is that of regularity. A classical example is Hilbert's XIXth problem (1900), solved by De Giorgi and Nash in 1956. During the second half of the XXth century, the regularity theory for elliptic and parabolic PDE's experienced a huge development, and many fundamental questions were answered by Caffarelli, Nirenberg, Krylov, Evans, Nadirashvili, Friedman, and many others. Still, there are problems of crucial importance that remain open. The aim of this project is to go significantly beyond the state of the art in some of the most important open questions in this context. In particular, three key objectives of the project are the following. First, to introduce new techniques to obtain fine description of singularities in nonlinear elliptic PDE's. Aside from its intrinsic interest, a good regularity theory for singular points is likely to provide insightful applications in other contexts. A second aim of the project is to establish generic regularity results for free boundaries and other PDE problems. The development of methods which would allow one to prove generic regularity results may be viewed as one of the greatest challenges not only for free boundary problems, but for PDE problems in general. Finally, the third main objective is to achieve a complete regularity theory for nonlinear elliptic PDE's that does not rely on monotonicity formulas. These three objectives, while seemingly different, are in fact deeply interrelated.

1 335 250 €

Start date: 2019-01-01, End date: 2023-12-31

The main objective of this research proposal is to explore the electrical properties of nanoscale devices and circuits based on nanolayers. Nanolayers cover a wide span of possible electronic properties, ranging from semiconducting to superconducting. The possibility to form electrical circuits by varying their geometry offers rich research and practical opportunities. Together with graphene, nanolayers could form the material library for future nanoelectronics where different materials could be mixed and matched to different functionalities.

1 799 996 €

Start date: 2009-09-01, End date: 2014-08-31

Using recent progress in laser technology and in particular in the field of ultra-fast lasers, we are getting close to accomplish the alchemist dream of transforming materials. Compact lasers can generate pulses with ultra-high peak powers in the Tera-Watt or even Peta-Watt ranges. These high-power pulses lead to a radically different laser-matter interaction than the one obtained with conventional lasers. Non-linear multi-photons processes are observed; they open new and exciting opportunities to tailor the matter in its intimate structure with sub-wavelength spatial resolutions and in the three dimensions. This project is aiming at exploring the use of these ultrafast lasers to locally tailor the physical properties of glass materials. More specifically, our objective is to create polymorphs embedded in bulk structures and to demonstrate their use as means to introduce new functionalities in the material. The long-term objective is to develop the scientific understanding and technological know-how to create three-dimensional objects with nanoscale features where optics, fluidics and micromechanical elements as well as active functions are integrated in a single monolithic piece of glass and to do so using a single process. This is a multidisciplinary research that pushes the frontier of our current knowledge of femtosecond laser interaction with glass to demonstrate a novel design platform for future micro-/nano- systems.

1 757 396 €

Start date: 2012-12-01, End date: 2017-11-30

The goal of the proposed project is to create a universal (AKSZ type) topological field theory with values in graph complexes, capturing the rational homotopy types of manifolds, configuration and embedding spaces. If successful, such a theory will unite certain areas of mathematical physics, topology, homological algebra and algebraic geometry. More concretely, from the physical viewpoint it would give a precise topological interpretation of a class of well studied topological field theories, as opposed to the current state of the art, in which these theories are defined by giving formulae without guarantees on the non-triviality of the produced invariants. From the topological viewpoint such a theory will provide new tools to study much sought after objects like configuration and embedding spaces, and tentatively also diffeomorphism groups, through small combinatorial models given by Feynman diagrams. In particular, this will unite and extend existing graphical models of configuration and embedding spaces due to Kontsevich, Lambrechts, Volic, Arone, Turchin and others. From the homological algebra viewpoint a field theory as above provides a wealth of additional algebraic structures on the graph complexes, which are some of the most central and most mysterious objects in the field. Such algebraic structures are expected to yield constraints on the graph cohomology, as well as ways to construct series of previously unknown classes.

1 162 500 €

Start date: 2016-07-01, End date: 2021-06-30

Digital 3D content creation and modeling has become an indispensable part of our technology-driven society. Any modern design and manufacturing process involves manipulation of digital 3D shapes. Many industries have been long expecting ubiquitous 3D as the next revolution in multimedia. Yet, contrary to “traditional” media such as digital music and video, 3D content creation and editing is not accessible to the general public, and 3D geometric data is not nearly as wide-spread as it has been anticipated. Despite extensive geometric modeling research in the past two decades, 3D modeling is still a restricted domain and demands tedious, time consuming and expensive work effort even from trained professionals, namely engineers, designers, and digital artists. Geometric modeling is reported to constitute one of the lowest-productivity components of product life cycle. The major reason for 3D shape modeling remaining inaccessible and tedious is that our current geometry representation and modeling algorithms focus on low-level mathematical properties of the shapes, entirely missing structural, contextual or semantic information. As a consequence, current modeling systems are unintuitive, inefficient and difficult for humans to work with. We believe that instead of continuing on the current incremental research path, a concentrated effort is required to fundamentally rethink the shape modeling process and re-align research agendas, putting high-level shape structure and function at the core. We propose a research plan that will lead to intelligent digital 3D modeling tools that integrate semantic knowledge about the objects being modeled and provide the user an intuitive and logical response, fostering creativity and eliminating unnecessary low-level manual modeling tasks. Achieving these goals will represent a fundamental change to our current notion of 3D modeling, and will finally enable us to leverage the true potential of digital 3D content for society.

1 497 442 €

Start date: 2012-09-01, End date: 2017-08-31

It is proposed to develop a novel instrument for angular resolved photoelectron spectroscopy (ARPES) by combining a laser based ultraviolet light source with a state-of-the-art electron spectrometer. This combination will be unique in Europe and will push this important technique to an entirely new level of resolution, comparable to the thermal broadening at 1 K and nearly an order of magnitude lower than the resolution achievable in practical ARPES experiments with the latest synchrotron light sources. The low photon energy of this new source will also markedly enhance the bulk sensitivity of ARPES and thus enable the investigation of interesting materials that were not accessible so far. These new capabilities will be used to study the subtle quantum many-body states of correlated electrons in transition metal oxides, a frontier topic in condensed-matter physics. Specifically, we will focus on electronic instabilities in perovskites and elucidate how different degrees of freedom play together to determine the often vastly different properties of chemically closely related materials. Moreover, we will apply modern electron spectroscopy to correlated molecular solids with complex phase diagrams that challenge existing theory for satisfactory explanations. This field is largely unexplored but is fundamental for advances in molecular electronics.

1 450 825 €

Start date: 2008-08-01, End date: 2013-07-31

"Coherent extreme ultraviolet (XUV) light sources open up new opportunities for science and technology. Promising examples are attosecond metrology, spectroscopic and structural analysis of matter on a nanometer scale, high resolution XUV-microscopy and lithography. The most promising technique for table-top sources is femtosecond laser-driven high-harmonic generation (HHG) in gases. Unfortunately, their XUV photon flux is not sufficient for most applications. This is caused by the low average power of the kHz repetition rate driving lasers (<10 W) and the poor conversion efficiency (<10-6). Following the traditional path of increasing the power, numerous research teams are engineering larger and more complex femtosecond high-power amplifier systems, which are supposed to provide several kilowatts of average power in the next decade. However, it is questionable if such systems can easily serve as tool for further scientific studies with XUV light. The goal of this proposal is the realization of a simpler and more efficient source of high-flux XUV radiation. Instead of amplifying a laser beam to several kW of power and dumping it after the HHG interaction, the generation of high harmonics is placed directly inside the intra-cavity multi-kilowatt beam of a femtosecond laser. Thus, the unconverted light is “recycled”, and the laser medium only needs to compensate for the low losses of the resonator. Achieving passive femtosecond pulse formation at these record-high power levels will require eliminating any destabilizing effects inside the resonator. This appears to be only feasible with ultrafast thin disk lasers, because all key components are used in reflection. Exploiting the scientific opportunities of the resulting table-top multi-MHz coherent XUV light source in various interdisciplinary applications is the second major part of this project. The developed XUV source will be transportable, which will enable the fast implementation of joint measurements."

1 500 000 €

Start date: 2012-03-01, End date: 2017-02-28

To study and understand the aggregation, nucleation, and/or self-assembly processes of crystalline matter is of crucial importance for research and applications in many disciplines. For example, understanding the formation of crystalline amyloid fibres could lead to advances in the treatment and prevention of both Alzheimer’s and Parkinson’s diseases, whereas controlling the process of crystal formation can play a significant role in obtaining chemicals and materials that are important for industry as well as society as a whole (e.g., drugs, superconductors, polarizers and/or frequency modulators). Despite the impressive progress made in molecular engineering during the last few decades, the quest for a general tool-box technology to study, control and monitor crystallisation processes as well as to isolate metastable states (dynamic capture) is still incomplete. That is because crystalline assemblies are frequently investigated in their equilibrium form, driving the system to its minimum energy state. This methodology limits the emergence of new chemicals and crystals with advanced functionalities, and thus hampers advances in the field of materials engineering. µ-CrysFact will develop tool-box technologies where diffusion-limited and kinetically controlled environments will be achieved during crystallisation and where the isolation of non-equilibrium species will be facilitated by pushing crystallisation processes out of equilibrium. In addition, µ-CrysFact’s technologies will be used to localise, integrate and chemically treat crystals with the aim of honing their functionality. This unprecedented approach has the potential to lead to the discovery of new materials with advanced functions and unique properties, thus opening new horizons in materials engineering research.

1 814 128 €

Start date: 2016-09-01, End date: 2021-08-31

Data exchange and data publishing is an inherent component of our interconnected world. Industrial companies outsource datasets to marketing and mining firms in order to support business intelligence; medical institutions exchange collected clinical experiments; academic institutions create repositories and share datasets for promoting research collaboration. A common denominator in any data exchange is the 'transformation' of the original data, which usually results in 'distortion' of data. While accurate and useful information can be potentially distilled from the original data, operations such as anonymization, rights protection and compression result in modified datasets that very seldom retain the mining capacity of its original source. This proposal seeks to address questions such as the following: - How can we lossy compress datasets and still guarantee that mining operations are not distorted? - Is it possible to right protect datasets and provide assurances that this task shall not impair our ability to distill useful knowledge? - To what extent can we resolve data anonymization issues and yet retain the mining capacity of the original dataset? We will examine a fundamental and hard problem in the area of knowledge discovery, which is the delicate balance between data transformation and data utility under mining operations. The problem lies at the confluence of many areas, such as machine and statistical learning, information theory, data representation and optimization. We will focus on studying data transformation methods (compression, anonymization, right protection) that guarantee the preservation of the salient dataset characteristics, such that data mining operations on original and transformed dataset are retained as well as possible. We will investigate how graph-centric approaches, clustering, classification and visualization algorithms can be ported to work under the proposed mining-preservation paradigm. Additional research challenges i

1 499 999 €

Start date: 2011-04-01, End date: 2016-03-31

The main goal of this project is to study the fundamental properties of field theories of space-time, their cosmological consequences and observational signatures. My approach aims to use the next generation of cosmological and astrophysical observations to test the validity of General Relativity on scales where it has not been fully tested yet and its resilience against alternative theories with modifications on cosmological scales. I will first study the implications of the quantum aspects of modified gravity theories beyond the tree level analyses for their viability, consistency and predictability. This will reduce the allowed alternative theories significantly. I will then investigate the physical consequences of these theoretically promising theories for cosmological and astrophysical scenarios. As part of my approach, I will use large galaxy surveys to constrain effects on the dynamics of cosmic structure formation from these modifications of gravity. In addition, I will confront modified theoretical predictions with Planck measurements of the Cosmic Microwave Background, type-Ia supernova data, measurements of the Baryon Acoustic Oscillations and gravitational lensing. Along the way, my group and I will crucially contribute to the development of the necessary analytical and numerical tools to exhaustively analyse such data in the search for modifications of gravity. In addition, the recent detection of gravitational waves by the LIGO team has paved an exciting new avenue for testing gravitational theories. These new observations will put even more stringent constraints on alternative theories. As part of the proposed research, I will also extensively exploit this new observational channel to test the validity of General Relativity and put new effects of modified gravity on trial. In particular, the propagation speed of tensor perturbations in modified gravity theories will be severely restricted by observations of gravitational waves.

1 500 000 €

Start date: 2019-01-01, End date: 2023-12-31

"Networks pervade every aspect of nowadays life. This is one of the reasons why their design, management, and analysis is one of the most active areas of theoretical and empirical research in Computer Science and Operations Research. The main goal of this project is to increase our theoretical understanding of networks, with a special focus on faster exact exponential-time algorithms and more accurate polynomial-time approximation algorithms for NP-hard network design problems. We will consider classic, challenging open problems in the literature, as well as new, exciting problems arising from the applications. These problems will be addressed with the most advanced algorithmic and analytical tools, including our recently developed techniques: iterative randomized rounding, core detouring, and randomized dissection. A second, ambitious goal of this project is to stimulate the interaction and cross-fertilization between exact and approximation algorithms. This might open new research horizons."

1 122 199 €

Start date: 2012-01-01, End date: 2016-12-31

"This proposal advocates a fundamentally new approach to achieving software quality: remove the distinction between software use and software testing -- enable programs to accumulate experience from each one of their executions, and leverage this experience toward self-improvement of the software. My hypothesis is that every program execution has information by-products that, if suitably captured and aggregated, can substantially speed up the process of testing programs and proving them correct. Software is being executed billions of times around the world, with the corresponding information going to waste. At the same time, traditional software testing tries to simulate a small subset of real-world conditions and executions. I propose instead viewing every execution of a program as a test run, and the aggregation of executions across the lifetime of all copies of that program as one gigantic test suite. I propose the study of techniques and formalisms for automatically recouping the information that is lost during everyday software use, aggregating it, and automatically turning it into tests and proofs; techniques to use these tests and proofs to automatically correct the behavior of programs; and techniques for automatically steering programs into exploring behaviors for which information is lacking. All these techniques will be embodied in a platform, called BeeNet, that implements a massively distributed learning process which turns execution by-products into a collective experience that leads to higher quality software. This is a radical new way of exploiting the vast (but today completely wasted) information that results from program execution. I will investigate these questions with an integrated approach that combines thorough theoretical studies with practical application to real-world software, employing the perspectives of three different research communities: operating systems, programming languages, and software verification."

1 334 977 €

Start date: 2012-02-01, End date: 2018-01-31

One of the most exciting areas of theoretical computer science is to understand the approximability of fundamental optimization problems. A prominent example is the traveling salesman problem, for which a long-standing conjecture states that a certain algorithm gives a better guarantee than current methods can prove. The resolution of this conjecture and of many other fundamental problems is intimately related to an increased understanding of strong convex relaxations. Although these problems have resisted numerous attempts, recent breakthrough results, in which the PI has played a central role, indicate new research directions with the potential to resolve some of our most exciting open questions. We propose three research directions to revolutionize our understanding of these problems and more generally of the use of convex relaxations in approximation algorithms: (I) develop new approaches to analyze and harness the power of existing convex relaxations; (II) understand the power of automatically generated relaxations; and (III) prove the optimality of algorithms based on convex relaxations. The proposed research lies in the frontier of approximation algorithms and optimization with connections to major problems in complexity theory, such as the unique games conjecture. Any progress will be a significant contribution to theoretical computer science and mathematical optimization.

1 451 052 €

Start date: 2014-01-01, End date: 2018-12-31

Discovering, classifying and understanding phases of quantum matter is a core goal of condensed matter physics. Next to the notion of symmetry breaking phases, the concept of topological phases of matter is a prevailing theme of recent research. Topological phases are envisioned for various applications due to their universal and robust properties, such as protected conducting boundary modes, and provoke fundamental questions about the nature of many-body quantum states by providing the basis for exotic quasiparticles. In this ERC research project, I propose several new topological phases and novel numerical approaches for studying and classifying the most sought-after topological phases of matter. Concretely, I propose the concept of three-dimensional hierarchical topological insulators, which, in contrast to the known topological phases, do not posses gapless surface, but protected gapless edge modes. Moreover, I plan to study topological metals arising in strongly correlated Kondo systems, going beyond the current paradigm of considering topological metals that arise in the absence of electronic correlations. Furthermore, I propose to make the analogous step for topological superconductors, which have been studied as free models to search for Majorana quasiparticles: For the first time, I want to explore strongly interacting systems that realize the more powerful parafermion quasiparticles with numerical techniques. Finally, in a cross-disciplinary and exploratory sub-project, I will employ methods of deep neural networks to classify strongly correlated quantum phases using supervised learning combined with a technique called deep dreaming. Each of these sub-projects has the potential to make a paradigm-changing contribution to the study of strongly correlated and topological states of quantum matter and the combination of them allows to take advantage of synergy effects and a balance between high-risk and definitely feasible key developments.

1 362 401 €

Start date: 2018-01-01, End date: 2022-12-31

In the last decades, the power to control photons and electrons paved the way for extraordinary technological developments in electronic and optoelectronic applications. The same degree of control is still lacking with quantized lattice vibrations, i.e. phonons. Phonons are the carriers of heat and sound. The understanding and ability to manipulate phonons as quantum particles in solids enable the control of coherent phonon transport, which is of fundamental interest and could also be exploited in applications. Logic operations can be realized with the manipulation of phonons both in their coherent and incoherent form in order to switch, amplify, and route signals, and to store information. If brought to a mature level, phononic devices can become complementary to the conventional electronics, opening new opportunities. I envision to realize each part of this technology exploiting phonons and to bring them together in an integrated circuit on chip: a phononic integrated circuit. The objective of the proposal is: A: the realization of coherent phonon source and detector; B: the realization of phonon computation with the use of thermal logic gates; C: the realization of phonon based quantum and thermal memories. To this end it is crucial to engineer nanoscale heterostructures with suitable interfaces, and to engineer the phonon spectrum and the interface thermal resistance. Phonons will be launched, probed and manipulated with a combination of pump-probe experiments and resistive thermal measurements on chip. The proposed research will be of great relevance for fundamental research as well as for technological applications in the field of sound and thermal management.

1 488 388 €

Start date: 2018-01-01, End date: 2022-12-31

"The term structure of interest rates plays a central role in the functioning of the interbank market. It also represents a key factor for the valuation and management of long term liabilities, such as pensions. The financial crisis has revealed the multivariate risk nature of the term structure, which includes inflation, credit and liquidity risk, resulting in multiple spread adjusted discount curves. This has generated a strong interest in tractable stochastic models for the movements of the term structure that can match all determining risk factors. We propose a new class of term structure models based on polynomial factor processes which are defined as jump-diffusions whose generator leaves the space of polynomials of any fixed degree invariant. The moments of their transition distributions are polynomials in the initial state. The coefficients defining this relationship are given as solutions of a system of nested linear ordinary differential equations. As a consequence polynomial processes yield closed form polynomial-rational expressions for the term structure of interest rates. Polynomial processes include affine processes, whose transition functions admit an exponential-affine characteristic function. Affine processes are among the most widely used models in finance to date, but come along with some severe specification limitations. We propose to overcome these shortcomings by studying polynomial processes and polynomial expansion methods achieving a comparable efficiency as Fourier methods in the affine case. In sum, the objectives of this project are threefold. First, we plan to develop a theory for polynomial processes and entirely explore their statistical properties. This fills a gap in the literature on affine processes in particular. Second, we aim to develop polynomial-rational term structure models addressing the new paradigm of multiple spread adjusted discount curves. Third, we plan to implement and estimate these models using real market data."

995 155 €

Start date: 2012-12-01, End date: 2017-11-30

"The Plateau's problem consists in finding the surface of least area spanning a given contour. This question has attracted the attention of many mathematicians in the last two centuries, providing a prototypical problem for several fields of research in mathematics. For hypersurfaces a lot is known about the existence and regularity thanks to the classical works of De Giorgi, Almgren, Fleming, Federer, Simons, Allard, Simon, Schoen and several other authors. In higher codimension a quite powerful existence theory, the ``theory of currents'', was developed by Federer and Fleming in 1960. The success of this theory relies on its homological flavor and indeed it has found several applications to problems in differential geometry. Many geometric objects which are widely studied in the modern literature are naturally area-minimizing currents: two examples among many are special lagrangians and holomorphic subvarieties. However the understanding of the regularity issues is, compared to the case of hypersurfaces, much poorer. Aside from its intrinsic interest, a good regularity theory is likely to provide more insightful geometric applications. A quite striking example is Taubes' proof of the equivalence between the Gromov and Seiberg-Witten invariants. A very complicated and far reaching regularity theory has been developed by Almgren thirty years ago in a monumental work of almost 1000 pages. The first part of this project aims at reaching the same conclusions of Almgren with a more flexible and accessible theory. In the second part I wish to go beyond Almgren's work and attack some of the many open questions which still remain in the field."

919 500 €

Start date: 2012-09-01, End date: 2017-08-31

"We address one of the fundamental challenges of our time: Acting effectively while facing a deluge of data. Massive volumes of data are generated from corporate and public sources every second, in social, scientific and commercial applications. In addition, more and more low level sensor devices are becoming available and accessible, potentially to the benefit of myriads of applications. However, access to the data is limited, due to computational, bandwidth, power and other limitations. Crucially, simply gathering data is not enough: we need to make decisions based on the information we obtain. Thus, one of the key problems is: How can we obtain most decision-relevant information at minimum cost? Most existing techniques are either heuristics with no guarantees, or do not scale to large problems. We recently showed that many information gathering problems satisfy submodularity, an intuitive diminishing returns condition. Its exploitation allowed us to develop algorithms with strong guarantees and empirical performance. However, existing algorithms are limited: they cannot cope with dynamic phenomena that change over time, are inherently centralized and thus do not scale with modern, distributed computing paradigms. Perhaps most crucially, they have been designed with the focus of gathering data, but not for making decisions based on this data. We seek to substantially advance large-scale adaptive decision making under partial observability, by grounding it in the novel computational framework of adaptive submodular optimization. We will develop fundamentally new scalable techniques bridging statistical learning, combinatorial optimization, probabilistic inference and decision theory to overcome the limitations of existing methods. In addition to developing novel theory and algorithms, we will demonstrate the performance of our methods on challenging real world interdisciplinary problems in community sensing, information retrieval and computational sustainability."

1 499 900 €

Start date: 2012-11-01, End date: 2017-10-31

In droplet-based microfluidics, the elementary units transporting reagents from one functional site to another (mixer, sensor or analyzer) are droplets, which are carried by an inert wetting fluid. This research project aims at the development of numerical models of flowing droplets in thin spatially extended microchannels, designed at avoiding the exponential complexity of parallelized 1-D networks. We aim at simulating the trajectory of droplets transported by a pressure-driven carrier fluid, as they evolve in a surface energy gradient, generated by channel depth variations or surface tension inhomogeneities. To this end, we exploit the remarkable aspect ratio of these microfluidic devices to propose a depth-averaged description of the pancake shaped droplets. The resulting equations, called Brinkman's equations, combine the 2D Stokes equations with 2D Darcy potential-flow-like equations. Their diphasic simulation relies on the adaptation of existing algorithms to this particular free interface problem. Pressure corrections due to the thickness variations of the lubricating thin films will also be included. Surfactant and heat dynamics will then be added to model thermo- and soluto-capillary forcing. The depth-averaged model will be finally generalized to account for arbitrary depth variations, so as to add dynamics to the quasi-static description of droplets moving along successive minimal surface energy locations. A specific part of the project is also devoted to the development of an experimental expertise: it is indeed essential to the success of the project to conduct fundamental microfluidic experiments in order to validate our new models. While SIMCOMICS aims at shrinking the gap between present computations of droplets flowing in microchannels and the increasing number of application-oriented experimental studies, it both raises fundamental questions and opens promising perspectives for the engineering design of new microcarved microchannels.

1 405 796 €

Start date: 2012-01-01, End date: 2016-12-31

"State-space search, finding paths in huge, implicitly given graphs, is a fundamental problem in artificial intelligence and other areas of computer science. State-space search algorithms like A*, IDA* and greedy best-first search are major success stories in artificial intelligence, and hundreds of papers based on variations of these algorithms are published every year. Due to this success, the major assumptions of these algorithms are rarely questioned. We argue that the current generation of state-space search algorithms has three significant deficiencies that impede further progress in the field: 1. They explore a monolithic model of the world rather than applying a factored perspective. 2. They do not learn from mistakes and hence tend do commit the same mistake thousands of times. 3. In the case of satisficing (i.e., suboptimal) search, the design of the major algorithms has been based on ad-hoc intuitions rather than sound theoretical principles. This proposal targets these three issues. We propose to develop a rigorous theory of factored state-space search, a rigorous theory of learning from information gathered during search, and a decision-theoretic foundation for satisficing search algorithms. Based on these insights we will design and implement new state-space search algorithms addressing the deficiencies of current methods. Finally, we will apply the new algorithms to application domains of state-space search to raise the state of the art in these areas."

1 499 737 €

Start date: 2014-02-01, End date: 2019-01-31

I will experimentally investigate hybrid superconductor/semiconductor devices for realizing novel topological states of matter, with interest both in fundamental physics and quantum computing applications. Common denominator of the proposed experiments is a regime where the characteristic energy scales of the system, namely Fermi energy, spin orbit interaction correction, superconducting gap and Zeeman splitting are comparable to each other, resulting in unique and mostly uncharted physical territories. Differently from the most widespread use of semiconductor nanowires coupled to superconductors, I will employ novel hybrid two-dimensional electron gases (2DEGs) where the superconductor is grown in-situ and matched to the semiconductor lattice. This novel system was mainly developed by the team I supervise, during the last two years. Compared to the conventional nanowire-based approach, hybrid 2DEGs are readily available, characterized by very low disorder and more amenable to complex sample designs. The work will focus on: 1) Taking full advantage of the planar geometry to study spatial and non-local properties of individual Majorana wires, as well as branched geometries. These experiments will constitute critical tests to establish if the commonly observed zero bias peaks are indeed associated with Majorana modes and pave the way to complex networks of interacting Majorana wires, a requirement for quantum computing. 2) Studying topological phenomena in multi-terminal Josephson junctions (JJs), with particular emphasis on tuning the superconducting phase difference across electrodes pairs. Topological JJs offer a new and possibly advantageous path forward to create and manipulate Majorana modes not explored up to date, including the possibility to reach the topological regime for vanishing small external magnetic fields, useful for applications. Success of the proposal will constitute a key step forward towards topological quantum computing.

1 999 916 €

Start date: 2019-03-01, End date: 2024-02-29

Nanotechnology is a new frontier in research and new tools must be developed. As surface to volume ratios become large, engineering at the nanoscale will be dominated by surface science. The study of Contact Mechanics at nanoscales nanotribology- needs to fully account for adhesive forces, third-body interactions and deformation mechanisms at contacting asperities. Understanding these factors as well as the morphological evolution of contact clusters has the potential of explaining the origins of frictional forces and wear. This will guide us in the design of tailored-made lubricants and surface morphologies, which, in turn, will help reduce the high societal cost of wear damage. This ERCstg proposal describes a plan to establish a world-leading group in Contact Mechanics at length scales ranging from the atomic to macroscopic scales relevant to Civil or Mechanical Engineering structural applications. Our approach will have recourse to molecular dynamics coupled with the finite-element method for an accurate description of atomic interactions at the contact surface, and of long-range elastic forces. The project is interdisciplinary as the deepening of our understanding of Contact Mechanics will necessitate Computer Science developments. A central objective of the research will be the release of an open, 3D parallel, finite-element platform dedicated to contact applications. The PI will assemble a team of Engineers and Computer Scientists to ensure a successful and perennial diffusion in the European academic and industrial network. The research will therefore explore the origins of friction, a scientific quest of fundamental importance to many industrial applications, and will also create a stable base for sharing scientific-computing resources.

1 773 000 €

Start date: 2009-09-01, End date: 2014-08-31

Ultrafast Spectroscopic Electron Diffraction (USED) of quantum solids and thin films

1 464 000 €

Start date: 2010-11-01, End date: 2015-10-31