ERC FUNDED PROJECTS

The scientific goal of the proposal is to answer central questions related to diffeomorphism groups of manifolds of dimension 2 and 3, and to their deformation invariant analogs, the mapping class groups. While the classification of surfaces has been known for more than a century, their automorphism groups have yet to be fully understood. Even less is known about diffeomorphisms of 3-manifolds despite much interest, and the objects here have only been classified recently, by the breakthrough work of Perelman on the Poincar\'e and geometrization conjectures. In dimension 2, I will focus on the relationship between mapping class groups and topological conformal field theories, with applications to Hochschild homology. In dimension 3, I propose to compute the stable homology of classifying spaces of diffeomorphism groups and mapping class groups, as well as study the homotopy type of the space of diffeomorphisms. I propose moreover to establish homological stability theorems in the wider context of automorphism groups and more general families of groups. The project combines breakthrough methods from homotopy theory with methods from differential and geometric topology. The research team will consist of 3 PhD students, and 4 postdocs, which I will lead.

724 992 €

Start date: 2009-11-01, End date: 2014-10-31

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

This project studies several mathematical topics with a related theme, all of them part of the relatively new discipline known as additive combinatorics. We look at approximate, or rough, variants of familiar mathematical notions such as group, polynomial or homomorphism. In each case we seek to describe the structure of these approximate objects, and then to give applications of the resulting theorems. This endeavour has already lead to groundbreaking results in the theory of prime numbers, group theory and combinatorial number theory.

1 000 000 €

Start date: 2011-10-01, End date: 2016-09-30

A central problem in developmental biology is to understand how tissues are patterned in time and space - how do identical cells differentiate to form the adult body plan? Patterns often arise from prior asymmetries in developing embryos, but there is also increasing evidence for self-organizing mechanisms that can break the symmetry of an initially homogeneous cell population. These patterning processes are mediated by a small number of signaling molecules, including the TGF-β superfamily members BMP and Nodal. While we have begun to analyze how biophysical properties such as signal diffusion and stability contribute to axis formation and tissue allocation during vertebrate embryogenesis, three key questions remain. First, how does signaling cross-talk control robust patterning in developing tissues? Opposing sources of Nodal and BMP are sufficient to produce secondary zebrafish axes, but it is unclear how the signals interact to orchestrate this mysterious process. Second, how do signaling systems self-organize to pattern tissues in the absence of prior asymmetries? Recent evidence indicates that axis formation in mammalian embryos is independent of maternal and extra-embryonic tissues, but the mechanism underlying this self-organized patterning is unknown. Third, what are the minimal requirements to engineer synthetic self-organizing systems? Our theoretical analyses suggest that self-organizing reaction-diffusion systems are more common and robust than previously thought, but this has so far not been experimentally demonstrated. We will address these questions in zebrafish embryos, mouse embryonic stem cells, and bacterial colonies using a combination of quantitative imaging, optogenetics, mathematical modeling, and synthetic biology. In addition to providing insights into signaling and development, this high-risk/high-gain approach opens exciting new strategies for tissue engineering by providing asymmetric or temporally regulated signaling in organ precursors.

1 997 750 €

Start date: 2020-07-01, End date: 2025-06-30