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

Extreme astrophysical events such as relativistic flows, cataclysmic explosions and black hole accretion are one of the key areas for astrophysics in the 21st century. The extremes of physics experienced in these environments are beyond anything achievable in any laboratory on Earth, and provide a unique glimpse at the laws of physics operating in extraordinary regimes. All of these events are associated with transient radio emission, a tracer both of the acceleration of particles to relativistic energies, and coherent emitting regions with huge effective temperatures. By studying radio bursts from these phenomena we can pinpoint the sources of explosive events, understand the budget of kinetic feedback by explosive events in the ambient medium, and probe the physical state of the universe back to the epoch of reionisation, less than a billion years after the big bang. In seeking to push back the frontiers of extreme astrophysics, I will use a trio of revolutionary new radio telescopes, LOFAR, ASKAP and MeerKAT, pathfinders for the Square Kilometre Array, and all facilities in which I have a major role in the search for transients. I will build an infrastructure which transforms their combined operations for the discovery, classification and reporting of transient astrophysical events, over the whole sky, making them much more than the sum of their parts. This will include development of environments for the coordinated handling of extreme astrophysical events, in real time, via automated systems, as well as novel techniques for the detection of these events in a sea of noise. I will furthermore augment this program by buying in as a major partner to a rapid-response robotic optical telescope, and by cementing my relationship with an orbiting X-ray facility. This multiwavelength dimension will secure the astrophysical interpretation of our observational results and help to revolutionise high-energy astrophysics via a strong scientific exploitation program.

2 999 847 €

Start date: 2011-07-01, End date: 2017-06-30

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