ERC FUNDED PROJECTS

For a large family of computational problems collectively known as constrained optimization and satisfaction problems (CSPs), four decades of research in algorithms and computational complexity have led to a theory that tries to classify them as algorithmically tractable vs. intractable, i.e. polynomial-time solvable vs. NP-hard. However, there remains an important gap in our knowledge in that many CSPs of interest resist classification by this theory. Some such problems of practical relevance include fundamental partition problems in graph theory, isomorphism problems in combinatorics, and strategy-design problems in mathematical game theory. To tackle this gap in our knowledge, the research of the last decade has been driven either by finding hard instances for algorithms that solve tighter and tighter relaxations of the original problem, or by formulating new hardness-hypotheses that are stronger but admittedly less robust than NP-hardness. The ultimate goal of this project is closing the gap between the partial progress that these approaches represent and the original classification project into tractable vs. intractable problems. Our thesis is that the field has reached a point where, in many cases of interest, the analysis of the current candidate algorithms that appear to solve all instances could suffice to classify the problem one way or the other, without the need for alternative hardness-hypotheses. The novelty in our approach is a program to develop our recent discovery that, in some cases of interest, two methods from different areas match in strength: indistinguishability pebble games from mathematical logic, and hierarchies of convex relaxations from mathematical programming. Thus, we aim at making significant advances in the status of important algorithmic problems by looking for a general theory that unifies and goes beyond the current understanding of its components.

1 725 656 €

Start date: 2015-06-01, End date: 2020-09-30

In order to celebrate mathematics in the new millennium, the Clay Mathematics Institute established seven $1.000.000 Prize Problems. One of these is the conjecture of Birch and Swinnerton-Dyer (BSD), widely open since the 1960's. The main object of this proposal is developing innovative and unconventional strategies for proving groundbreaking results towards the resolution of this problem and their generalizations by Bloch and Kato (BK). Breakthroughs on BSD were achieved by Coates-Wiles, Gross, Zagier and Kolyvagin, and Kato. Since then, there have been nearly no new ideas on how to tackle BSD. Only very recently, three independent revolutionary approaches have seen the light: the works of (1) the Fields medalist Bhargava, (2) Skinner and Urban, and (3) myself and my collaborators. In spite of that, our knowledge of BSD is rather poor. In my proposal I suggest innovating strategies for approaching new horizons in BSD and BK that I aim to develop with the team of PhD and postdoctoral researchers that the CoG may allow me to consolidate. The results I plan to prove represent a departure from the achievements obtained with my coauthors during the past years: I. BSD over totally real number fields. I plan to prove new ground-breaking instances of BSD in rank 0 for elliptic curves over totally real number fields, generalizing the theorem of Kato (by providing a new proof) and covering many new scenarios that have never been considered before. II. BSD in rank r=2. Most of the literature on BSD applies when r=0 or 1. I expect to prove p-adic versions of the theorems of Gross-Zagier and Kolyvagin in rank 2. III. Darmon's 2000 conjecture on Stark-Heegner points. I plan to prove Darmon’s striking conjecture announced at the ICM2000 by recasting it in terms of special values of p-adic L-functions.

1 428 588 €

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

Naturally-emitted very short-lived halogens (VSLH) have a profound impact on the chemistry and composition of the atmosphere, destroying greenhouse gases and altering aerosol production, which together can change the Earth´s radiative balance. Therefore, natural halogens possess leverage to influence climate, although their contribution to climate change is not well established and most climate models have yet to consider their effects. Also, there is increasing evidence that natural halogens i) impact on the air quality of coastal cities, ii) accelerates the atmospheric deposition of mercury (a toxic heavy metal) and iii) that their natural ocean and ice emissions are controlled by biological and photochemical mechanisms that may respond to climate changes. Motivated by the above, this project aims to quantify the so far unrecognized natural halogen-climate feedbacks and the impact of these feedbacks on global atmospheric oxidizing capacity (AOC) and radiative forcing (RF) across pre-industrial, present and future climates. Answering these questions is essential to predict if these climate-mediated feedbacks can reduce or amplify future climate change. To this end we will develop a multidisciplinary research approach using laboratory and field observations and models interactively that will allow us to peel apart the detailed physical processes behind the contribution of natural halogens to global climate change. Furthermore, the work plan also involves examining past-future climate impacts of natural halogens within a holistic Earth System model, where we will develop the multidirectional halogen interactions in the land-ocean-ice-biosphere-atmosphere coupled system. This will provide a breakthrough in our understanding of the importance of these natural processes for the composition and oxidation capacity of the Earth´s atmosphere and climate, both in the presence and absence of human influence.

1 979 112 €

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

Inflammatory diseases affect over 80 million people worldwide and accompany many diseases of industrialized countries, being the majority of them infection-free conditions. There are few efficient anti-inflammatory drugs to treat chronic inflammation and thus, there is an urgent need to validate novel targets. We now know that innate immunity is the main coordinator and driver of inflammation. Recently, we and others have shown that the activation of purinergic P2X7 receptors (P2X7R) in immune cells is a novel and increasingly validated pathway to initiate inflammation through the activation of the NLRP3 inflammasome and the release of IL-1β and IL-18 cytokines. However, how NLRP3 sense P2X7R activation is not fully understood. Furthermore, extracellular ATP, the physiological P2X7R agonist, is a crucial danger signal released by injured cells, and one of the most important mediators of infection-free inflammation. We have also identified novel signalling roles for P2X7R independent on the NLRP3 inflammasome, including the release of proteases or inflammatory lipids. Therefore, P2X7R has generated increasing interest as a therapeutic target in inflammatory diseases, being drug like P2X7R antagonist in clinical trials to treat inflammatory diseases. However, it is often questioned the functionality of P2X7R in vivo, where it is thought that extracellular ATP levels are below the threshold to activate P2X7R. The overall significance of this proposal relays to elucidate how extracellular ATP controls host-defence in vivo, ultimately depicting P2X7R signalling through and beyond inflammasome activation. We foresee that our results will generate a leading innovative knowledge about in vivo extracellular ATP signalling during the host response to infection and sterile danger.

1 794 948 €

Start date: 2014-09-01, End date: 2019-08-31

Multicore processors are present nowadays in most digital devices, from smartphones to high-performance servers. The increasing computational power of these processors is essential for enabling many important emerging application domains such as big-data, media, medical, or scientific modeling. A fundamental technique to improve performance is speculation, a technique that consists in executing work before it is known if it is actually needed. In hardware, speculation significantly increases energy consumption by performing unnecessary operations, while speculation in software (e.g., compilers) is not the default thus preventing performance optimizations. Since performance in current multicores is limited by their power budget, it is imperative to make multicores as energy-efficient as possible to increase performance even further. In a multicore architecture, the cache coherence protocol is an essential component since its unique but challenging role is to offer a simple and unified view of the memory hierarchy. This project envisions that extending the role of the coherence protocol to simplify other system components will be the key to overcome the performance and energy limitations of current multicores. In particular, ECHO proposes to add simple but effective extensions to the cache coherence protocol in order to (i) reduce and even eliminate misspeculations at the processing cores and synchronization mechanisms and to (ii) enable speculative optimizations at compile time. The goal of this innovative approach is to improve the performance and energy efficiency of future multicore architectures. To accomplish the objectives proposed in this project, I will build on my 14 years expertise in cache coherence, documented in over 40 publications of high impact.

1 999 955 €

Start date: 2019-09-01, End date: 2024-08-31

Extreme events often cause local-initial damage to the critical elements of building structures, followed by a cascade of further failures in the rest of the building; a phenomenon known as “progressive collapse”. Current design philosophies are based on giving buildings extensive continuity, so that when a critical element fails its load can be re-distributed among the rest of the structure. However, in certain situations (e.g. initial failure of several columns) this extensive continuity introduces undesirable effects and actually increases the risk of progressive collapse. Segmenting a building into individual units connected only by means of fuses would avoid a failure in one zone propagating to others. While such fuses would provide continuity for normal loads or small local-initial failure, they would “isolate” the different parts of the building when otherwise the forces generated by the initial failure would pull down the rest of the structure. Although fuse segmentation is probably the only alternative that can fill the gaps in the present design philosophies, so far, no studies have been carried out on the possibility of applying it to buildings. Endure’s overall aim is to develop a novel fuse-based segmentation design approach to limit or arrest the propagation of failures in building structures subjected to extreme events. The project will be multidisciplinary and highly ambitious, and will achieve its overall aim by: 1) Developing a performance-based approach for the design of fuse-segmented buildings; 2) Designing, manufacturing and testing fuses for segmenting buildings; and 3) Implementing fuses in segmented realistic building prototypes and testing and validating the new fuse-based approach in these structures. Endure will open up a new research area and design approach, and also deliver novel construction procedures. The project will lead to safer buildings, especially in the case of extreme events with severe consequences for building integrity.

2 509 375 €

Start date: 2022-01-01, End date: 2026-12-31

The epithelium is a cohesive two-dimensional layer of cells attached to a fluid-filled fibrous matrix, which lines most free surfaces and cavities of the body. It serves as a protective barrier with tunable permeability, which must retain integrity in a mechanically active environment. Paradoxically, it must also be malleable enough to self-heal and remodel into functional 3D structures such as villi in our guts or tubular networks. Intrigued by these conflicting material properties, the main idea of this proposal is to view epithelial monolayers as living engineering materials. Unlike lipid bilayers or hydrogels, widely used in biotechnology, cultured epithelia are only starting to be integrated in organ-on-chip microdevices. As for any complex inert material, this program requires a fundamental understanding of the structure-property relationships. (1) Regarding their effective in-plane rheology, at short time-scales epithelia exhibit solid-like behavior while at longer times they flow as a consequence of the only qualitatively understood dynamics of the cell-cell junctional network. (2) As for material failure, excessive tension can lead to epithelial fracture, but as we have recently shown, matrix poroelasticity can also cause hydraulic fracture under stretch. However, it is largely unknown how adhesion molecules, membrane, cytoskeleton and matrix interact to give epithelia their robust and flaw-tolerant resilience. (3) Regarding shaping 3D epithelial structures, besides the classical view of chemical patterning, mechanical buckling is emerging as a major morphogenetic driving force, suggesting that it may be possible design 3D epithelial structures in vitro by mechanical self-assembly. Towards understanding (1,2,3), we will combine a broad range of theoretical, computational and experimental methods. Besides providing fundamental mechanobiological understanding, this project will provide a framework to manipulate epithelia in bioinspired technologies.

1 989 875 €

Start date: 2016-09-01, End date: 2022-08-31

This project aims to go significantly beyond the state of the art in several fundamental questions in PDEs with a clear geometric flavor. Central to this proposal is the Euler equation for an incompressible fluid, where the topics that I will be concerned with range from free boundary problems where I will strive to prove that the curvature of the interface blows up in finite time due to the appearance of kinks of controlled geometry, to the existence of smooth stationary solutions that feature chaotic trajectories confined in knotted vortex tubes of any topology, as conjectured by V.I. Arnold over fifty years ago. I will also consider a number of questions in spectral theory about the geometry of the eigenfunctions of the Laplacian and of the curl operator (the so called Beltrami fields, of crucial importance in the study of stationary Euler flows), analyze the process of creation and destruction of vortex structures in the 3D Navier-Stokes and Gross-Pitaevskii equations, consider blowup problems in magnetohydrodynamics, develop global approximation theorems for dispersive equations, and study the limiting measures of a sequence of solutions to the Seiberg-Witten equation. Key for the feasibility of this deep, ambitious project is that these topics are by no means disjoint, so some common themes and fundamental ideas keep coming up in protean forms throughout the research project, and that I have already achieved major results in essentially all the topics covered in the proposal. This includes the proofs of well-known conjectures in fluid mechanics and spectral theory due to Lord Kelvin (1875), V.I. Arnold (1965), S.T. Yau (1993) and M. Berry (2001). The award of a Consolidator Grant would allow me to consolidate both my position as a leader in my fields of interest and the top-level research group on these topics that I am building.

1 825 163 €

Start date: 2021-03-01, End date: 2026-02-28

Soil dust aerosols are mixtures of different minerals, whose relative abundances, particle size distribution (PSD), shape, surface topography and mixing state influence their effect upon climate. However, Earth System Models typically assume that dust aerosols have a globally uniform composition, neglecting the known regional variations in the mineralogy of the sources. The goal of FRAGMENT is to understand and constrain the global mineralogical composition of dust along with its effects upon climate. The representation of the global dust mineralogy is hindered by our limited knowledge of the global soil mineral content and our incomplete understanding of the emitted dust PSD in terms of its constituent minerals that results from the fragmentation of soil aggregates during wind erosion. The emitted PSD affects the duration of particle transport and thus each mineral’s global distribution, along with its specific effect upon climate. Coincident observations of the emitted dust and soil PSD are scarce and do not characterize the mineralogy. In addition, the existing theoretical paradigms disagree fundamentally on multiple aspects. We will contribute new fundamental understanding of the size-resolved mineralogy of dust at emission and its relationship with the parent soil, based on an unprecedented ensemble of measurement campaigns that have been designed to thoroughly test our theoretical hypotheses. To improve knowledge of the global soil mineral content, we will evaluate and use available remote hyperspectral imaging, which is unprecedented in the context of dust modelling. Our new methods will anticipate the coming innovation of retrieving soil mineralogy through high-quality spaceborne hyperspectral measurements. Finally, we will generate integrated and quantitative knowledge of the role of dust mineralogy in dust-radiation, dust-chemistry and dust-cloud interactions based on modeling experiments constrained with our theoretical innovations and field measurements.

2 000 000 €

Start date: 2018-10-01, End date: 2023-09-30