ERC FUNDED PROJECTS

The traditional (Riemann) approach to analytic number theory uses the zeros of zeta functions. This requires the associated multiplicative function, say f(n), to have special enough properties that the associated Dirichlet series may be analytically continued. In this proposal we continue to develop an approach which requires less of the multiplicative function, linking the original question with the mean value of f. Such techniques have been around for a long time but have generally been regarded as “ad hoc”. In this project we aim to show that one can develop a coherent approach to the whole subject, not only reproving all of the old results, but also many new ones that appear inaccessible to traditional methods. Our first goal is to complete a monograph yielding a reworking of all the classical theory using these new methods and then to push forward in new directions. The most important is to extend these techniques to GL(n) L-functions, which we hope will now be feasible having found the correct framework in which to proceed. Since we rarely know how to analytically continue such L-functions this could be of great benefit to the subject. We are developing the large sieve so that it can be used for individual moduli, and will determine a strong form of that. Also a new method to give asymptotics for mean values, when they are not too small. We wish to incorporate techniques of analytic number theory into our theory, for example recent advances on mean values of Dirichlet polynomials. Also the recent breakthroughs on the sieve suggest strong links that need further exploration. Additive combinatorics yields important results in many areas. There are strong analogies between its results, and those for multiplicative functions, especially in large value spectrum theory, and its applications. We hope to develop these further. Much of this is joint work with K Soundararajan of Stanford University.

2 011 742 €

Start date: 2015-08-01, End date: 2020-07-31

Naturally occurring optical phenomena attract great attention and transform our ability to study biological processes, with “the discovery and development of the green fluorescent protein (GFP)” (Nobel Prize in Chemistry 2008) being a particularly successful example. Although found only in very few species in nature, most organisms can be genetically programmed to produce the brightly fluorescent GFP molecules. Combined with modern fluorescence detection schemes, this has led to entirely new ways of monitoring biological processes. The applicant now demonstrated a biological laser – a completely novel, living source of coherent light based on a single biological cell bioengineered to produce GFP. Such a laser is intrinsically biocompatible, thus offering unique properties not shared by any existing laser. However, the physical processes involved in lasing from GFP remain poorly understood and so far biological lasers rely on bulky, impractical external resonators for optical feedback. Within this project, the applicant and his team will develop for the first time an understanding of stimulated emission in GFP and related proteins and create an unprecedented stand-alone single-cell biolaser based on intracellular optical feedback. These lasers will be deployed as microscopic and biocompatible imaging probes, thus opening in vivo microscopy to dense wavelength-multiplexing and enabling unmatched sensing of biomolecules and mechanical pressure. The evolutionarily evolved nano-structure of GFP will also enable novel ways of studying strong light-matter coupling and will bio-inspire advances of synthetic emitters. The proposed project is inter-disciplinary by its very nature, bridging photonics, genetic engineering and material science. The applicant’s previous pioneering work and synergies with work on other lasers developed at the applicant’s host institution provide an exclusive competitive edge. ERC support would transform this into a truly novel field of research.

1 499 875 €

Start date: 2015-06-01, End date: 2020-05-31

Algorithms for Complex Collective Decisions on Structured Domains. The aim of this proposal is to substantially advance the field of Computational Social Choice, by developing new tools and methodologies that can be used for making complex group decisions in rich and structured environments. We consider settings where each member of a decision-making body has preferences over a finite set of alternatives, and the goal is to synthesise a collective preference over these alternatives, which may take the form of a partial order over the set of alternatives with a predefined structure: examples include selecting a fixed-size set of alternatives, a ranking of the alternatives, a winner and up to two runner-ups, etc. We will formulate desiderata that apply to such preference aggregation procedures, design specific procedures that satisfy as many of these desiderata as possible, and develop efficient algorithms for computing them. As the latter step may be infeasible on general preference domains, we will focus on identifying the least restrictive domains that enable efficient computation, and use real-life preference data to verify whether the associated restrictions are likely to be satisfied in realistic preference aggregation scenarios. Also, we will determine whether our preference aggregation procedures are computationally resistant to malicious behavior. To lower the cognitive burden on the decision-makers, we will extend our procedures to accept partial rankings as inputs. Finally, to further contribute towards bridging the gap between theory and practice of collective decision making, we will provide open-source software implementations of our procedures, and reach out to the potential users to obtain feedback on their practical applicability.

1 395 933 €

Start date: 2015-07-01, End date: 2020-06-30

Elucidating how neural circuits coordinate behaviour, and how molecules underpin the properties of individual neurons are major goals of neuroscience. Optogenetics and neural imaging combined with the powerful genetics and well-described nervous system of C. elegans offer special opportunities to address these questions. Previously, we identified a series of sensory neurons that modulate aggregation of C. elegans. These include neurons that respond to O2, CO2, noxious cues, satiety state, and pheromones. We propose to take our analysis to the next level by dissecting how, in mechanistic molecular terms, these distributed inputs modify the activity of populations of interneurons and motoneurons to coordinate group formation. Our strategy is to develop new, highly parallel approaches to replace the traditional piecemeal analysis. We propose to: 1) Harness next generation sequencing (NGS) to forward genetics, rapidly to identify a molecular ¿parts list¿ for aggregation. Much of the genetics has been done: we have identified almost 200 mutations that inhibit or enhance aggregation but otherwise show no overt phenotype. A pilot study of 50 of these mutations suggests they identify dozens of genes not previously implicated in aggregation. NGS will allow us to molecularly identify these genes in a few months, providing multiple entry points to study molecular and circuitry mechanisms for behaviour. 2) Develop new methods to image the activity of populations of neurons in immobilized and freely moving animals, using genetically encoded indicators such as the calcium sensor cameleon and the voltage indicator mermaid. This will be the first time a complex behaviour has been dissected in this way. We expect to identify novel conserved molecular and circuitry mechanisms.

2 439 996 €

Start date: 2011-04-01, End date: 2017-03-31