ERC FUNDED PROJECTS

I propose to investigate the nanometer scale organization of delicate 2-dimensional molecular materials using nanoscale vibrational spectroscopy. 2D structures are of great scientific and technological importance, for example as novel materials (graphene, MoS2, WS2, etc.), and in the form of biological membranes and synthetic 2D-polymers. Powerful methods for their analysis and imaging with molecular selectivity and sufficient spatial resolution, however, are lacking. Tip-enhanced Raman spectroscopy (TERS) allows label-free spectroscopic identification of molecular species, with ≈10 nm spatial resolution, and with single molecule sensitivity for strong Raman scatterers. So far, however, TERS is not being carried out in liquids, which is the natural environment for membranes, and its application to poor Raman scatterers such as components of 2D polymers, lipids, or other membrane compounds (proteins, sugars) is difficult. TERS has the potential to overcome the restrictions of other optical/spectroscopic methods to study 2D materials, namely (i) insufficient spatial resolution of diffraction-limited optical methods; (ii) the need for labelling for all methods relying on fluorescence; and (iii) the inability of some methods to work in liquids. I propose to address a number of scientific questions associated with the spatial organization, and the occurrence of defects in sensitive 2D molecular materials. The success of these studies will also rely critically on technical innovations of TERS that notably address the problem of energy dissipation. This will for the first time allow its application to study of complex, delicate 2D molecular systems without photochemical damage.

2 311 696 €

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

Faithful repair of double stranded DNA breaks (DSBs) is essential, as they are at the origin of genome instability, chromosomal translocations and cancer. Cells repair DSBs through different pathways, which can be faithful or mutagenic, and the balance between them at a given locus must be tightly regulated to preserve genome integrity. Although, much is known about DSB repair factors, how the choice between pathways is controlled within the nuclear environment is not understood. We have shown that nuclear architecture and non-random genome organization determine the frequency of chromosomal translocations and that pathway choice is dictated by the spatial organization of DNA in the nucleus. Nevertheless, what determines which pathway is activated in response to DSBs at specific genomic locations is not understood. Furthermore, the impact of 3D-genome folding on the kinetics and efficiency of DSB repair is completely unknown. Here we aim to understand how nuclear compartmentalization, chromatin structure and genome organization impact on the efficiency of detection, signaling and repair of DSBs. We will unravel what determines the DNA repair specificity within distinct nuclear compartments using protein tethering, promiscuous biotinylation and quantitative proteomics. We will determine how DNA repair is orchestrated at different heterochromatin structures using a CRISPR/Cas9-based system that allows, for the first time robust induction of DSBs at specific heterochromatin compartments. Finally, we will investigate the role of 3D-genome folding in the kinetics of DNA repair and pathway choice using single nucleotide resolution DSB-mapping coupled to 3D-topological maps. This proposal has significant implications for understanding the mechanisms controlling DNA repair within the nuclear environment and will reveal the regions of the genome that are susceptible to genomic instability and help us understand why certain mutations and translocations are recurrent in cancer

1 999 750 €

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

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: 2022-08-31

The goal of this project is to investigate two conjectures in arithmetic geometry pertaining to the geometry of projective varieties over finite and number fields. These two conjectures, formulated by Tate and Grothendieck in the 1960s, predict which cohomology classes are chern classes of line bundles. They both form an arithmetic counterpart of a theorem of Lefschetz, proved in the 1940s, which itself is the only known case of the Hodge conjecture. These two long-standing conjectures are one of the aspects of a more general web of questions regarding the topology of algebraic varieties which have been emphasized by Grothendieck and have since had a central role in modern arithmetic geometry. Special cases of these conjectures, appearing for instance in the work of Tate, Deligne, Faltings, Schneider-Lang, Masser-Wüstholz, have all had important consequences. My goal is to investigate different lines of attack towards these conjectures, building on recent work on myself and Jean-Benoît Bost on related problems. The two main directions of the proposal are as follows. Over finite fields, the Tate conjecture is related to finiteness results for certain cohomological objects. I want to understand how to relate these to hidden boundedness properties of algebraic varieties that have appeared in my recent geometric proof of the Tate conjecture for K3 surfaces. The existence and relevance of a theory of Donaldson invariants for moduli spaces of twisted sheaves over finite fields seems to be a promising and novel direction. Over number fields, I want to combine the geometric insight above with algebraization techniques developed by Bost. In a joint project, we want to investigate how these can be used to first understand geometrically major results in transcendence theory and then attack the Grothendieck period conjecture for divisors via a number-theoretic and complex-analytic understanding of universal vector extensions of abelian schemes over curves.

1 222 329 €

Start date: 2016-12-01, End date: 2021-11-30