ERC FUNDED PROJECTS

The proposal consists of an extensive research program to advance the understanding of singular integral operators of Harmonic Analysis in various situations on the borderline of the existing theory. This is to be achieved by a creative combination of techniques from Analysis and Probability. On top of the standard arsenal of modern Harmonic Analysis, the main probabilistic tools are the martingale transform inequalities of Burkholder, and random geometric constructions in the spirit of the random dyadic cubes introduced to Nonhomogeneous Analysis by Nazarov, Treil and Volberg. The problems to be addressed fall under the following subtitles, with many interconnections and overlap: (i) sharp weighted inequalities; (ii) nonhomogeneous singular integrals on metric spaces; (iii) local Tb theorems with borderline assumptions; (iv) functional calculus of rough differential operators; and (v) vector-valued singular integrals. Topic (i) is a part of Classical Analysis, where new methods have led to substantial recent progress, culminating in my solution in July 2010 of a celebrated problem on the linear dependence of the weighted operator norm on the Muckenhoupt norm of the weight. The proof should be extendible to several related questions, and the aim is to also address some outstanding open problems in the area. Topics (ii) and (v) deal with extensions of the theory of singular integrals to functions with more general domain and range spaces, allowing them to be abstract metric and Banach spaces, respectively. In case (ii), I have recently been able to relax the requirements on the space compared to the established theories, opening a new research direction here. Topics (iii) and (iv) are concerned with weakening the assumptions on singular integrals in the usual Euclidean space, to allow certain applications in the theory of Partial Differential Equations. The goal is to maintain a close contact and exchange of ideas between such abstract and concrete questions.

1 100 000 €

Start date: 2011-11-01, End date: 2016-10-31

Atmospheric aerosol particles and trace gases affect the quality of our life in many ways (e.g. health effects, changes in climate and hydrological cycle). Trace gases and atmospheric aerosols are tightly connected via physical, chemical, meteorological and biological processes occurring in the atmosphere and at the atmosphere-biosphere interface. One important phenomenon is atmospheric aerosol formation, which involves the production of nanometer-size particles by nucleation and their growth to detectable sizes. The main scientific objectives of this project are 1) to quantify the mechanisms responsible for atmospheric new particle formation and 2) to find out how important this process is for the behaviour of the global aerosol system and, ultimately, for the whole climate system. Our scientific plan is designed as a research chain that aims to advance our understanding of climate and air quality through a series of connected activities. We start from molecular simulations and laboratory measurements to understand nucleation and aerosol thermodynamic processes. We measure nanoparticles and atmospheric clusters at 15-20 sites all around the world using state of the art instrumentation and study feedbacks and interactions between climate and biosphere. With these atmospheric boundary layer studies we form a link to regional-scale processes and further to global-scale phenomena. In order to be able to simulate global climate and air quality, the most recent progress on this chain of processes must be compiled, integrated and implemented in Climate Change and Air Quality numerical models via novel parameterizations.

2 000 000 €

Start date: 2009-01-01, End date: 2013-12-31

BioELCell will deliver ground-breaking approaches to create next material generation based on renewable resources, mainly cellulose and lignin micro- and nano-particles (MNC, MNL). Our action will disassemble and re-engineer these plant-based polymers into functional materials that will respond to the demands of the bioeconomy of the future, critically important to Europe and the world. My ambitious, high gain research plan is underpinned in the use of multiphase systems with ultra-low interfacial tension to facilitate nanocellulose liberation and atomization of lignin solution streams into spherical particles. BioELCell will design novel routes to control MNC and MNL reassembly in new 1-D, 2-D and 3-D structures. The systematic methodologies that I propose will address the main challenges for lignocellulose processing and deployment, considering the important effects of interactions with water. This BioELCell action presents a transformative approach by integrating complementary disciplines that will lead to a far-reaching understanding of lignocellulosic biopolymers and solve key challenges in their use, paving the way to functional product development. Results of this project permeates directly or indirectly in the grand challenges for engineering, namely, water use, carbon sequestration, nitrogen cycle, food and advanced materials. Indeed, after addressing the key fundamental elements of the research lines, BioELCell vindicates such effects based on rational use of plant-based materials as a sustainable resource, making possible the generation of new functions and advanced materials. BioELCell goes far beyond what is known today about cellulose and lignin micro and nano-particles, some of the most promising materials of our century, which are emerging as key elements for the success of a sustainable society.

2 486 182 €

Start date: 2018-08-01, End date: 2023-07-31

"Large bodies usually follow the classical equations of motion. Deviations from this can be called macroscopic quantum behavior. These phenomena have been experimentally verified with cavity Quantum Electro Dynamics (QED), trapped ions, and superconducting Josephson junction systems. Recently, evidence was obtained that also moving objects can display such behavior. These objects are micromechanical resonators (MR), which can measure tens of microns in size and are hence quite macroscopic. The degree of freedom is their vibrations: phonons. I propose experimental research in order to push quantum mechanics closer to the classical world than ever before. I will try find quantum behavior in the most classical objects, that is, slowly moving bodies. I will use MR's, accessed via electrical resonators. Part of it will be in analogy to the previously studied macroscopic systems, but with photons replaced by phonons. The experiments are done in a cryogenic temperature mostly in dilution refrigerator. The work will open up new perspectives on how nature works, and can have technological implications. The first basic setup is the coupling of MR to microwave cavity resonators. This is a direct analogy to optomechanics, and can be called circuit optomechanics. The goals will be phonon state transfer via a cavity bus, construction of squeezed states and of phonon-cavity entanglement. The second setup is to boost the optomechanical coupling with a Josephson junction system, and reach the single-phonon strong-coupling for the first time. The third setup is the coupling of MR to a Josephson junction artificial atom. Here we will access the MR same way as the motion of a trapped ions is coupled to their internal transitions. In this setup, I am proposing to construct exotic quantum states of motion, and finally entangle and transfer phonons over mm-distance via cavity-coupled qubits. I believe within the project it is possible to perform rudimentary Bell measurement with phonons."

2 004 283 €

Start date: 2015-01-01, End date: 2019-12-31