ERC FUNDED PROJECTS

"This proposal develops a unified, underpinning technology to create novel, complex and biomimetic 3D environments for the control of tissue growth. As director of Cambridge Centre for Medical Materials, I have recently been approached by medical colleagues to help to solve important problems in the separate therapeutic areas of breast cancer, cardiac disease and blood disorders. In each case, the solution lies in complex 3D engineered environments for cell culture. These colleagues make it clear that existing 3D scaffolds fail to provide the required complex orientational and spatial anisotropy, and are limited in their ability to impart appropriate biochemical and mechanical cues. I have a strong track record in this area. A particular success has been the use of a freeze drying technology to make collagen based porous implants for the cartilage-bone interface in the knee, which has now been commercialised. The novelty of this proposal lies in the broadening of the established scientific base of this technology to enable biomacromolecular structures with: (A) controlled and complex pore orientation to mimic many normal multi-oriented tissue structures (B) compositional and positional control to match varying local biochemical environments, (C) the attachment of novel peptides designed to control cell behaviour, and (D) mechanical control at both a local and macroscopic level to provide mechanical cues for cells. These will be complemented by the development of (E) robust characterisation methodologies for the structures created. These advances will then be employed in each of the medical areas above. This approach is highly interdisciplinary. Existing working relationships with experts in each medical field will guarantee expertise and licensed facilities in the required biological disciplines. Funds for this proposal would therefore establish a rich hub of mutually beneficial research and opportunities for cross-disciplinary sharing of expertise."

2 486 267 €

Start date: 2013-04-01, End date: 2018-03-31

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: 2021-05-31

I propose to establish a research group to develop completely new tools in order to solve three important problems on the relationships between automorphic forms and Galois representations, which lie at the heart of the Langlands program. The first is to prove Serre’s conjecture for real quadratic fields. I will use automorphic induction to transfer the problem to U(4) over the rational numbers, where I will use automorphy lifting theorems and results on the weight part of Serre's conjecture that I established in my earlier work to reduce the problem to proving results in small weight and level. I will prove these base cases via integral p-adic Hodge theory and discriminant bounds. The second is to develop a geometric theory of moduli spaces of mod p and p-adic Galois representations, and to use it to establish the Breuil–Mézard conjecture in arbitrary dimension, by reinterpreting the conjecture in geometric terms. This will transform the subject by building the first connections between the p-adic Langlands program and the geometric Langlands program, providing an entirely new world of techniques for number theorists. As a consequence of the Breuil-Mézard conjecture, I will be able to deduce far stronger automorphy lifting theorems (in arbitrary dimension) than those currently available. The third is to completely determine the reduction mod p of certain two-dimensional crystalline representations, and as an application prove a strengthened version of the Gouvêa–Mazur conjecture. I will do this by means of explicit computations with the p-adic local Langlands correspondence for GL_2(Q_p), as well as by improving existing arguments which prove multiplicity one theorems via automorphy lifting theorems. This work will show that the existence of counterexamples to the Gouvêa-Mazur conjecture is due to a purely local phenomenon, and that when this local obstruction vanishes, far stronger conjectures of Buzzard on the slopes of the U_p operator hold.

1 131 339 €

Start date: 2012-10-01, End date: 2017-09-30

Many parts of Graph Theory have witnessed a huge growth over the last years, partly because of their relation to Theoretical Computer Science and Statistical Physics. These connections arise because graphs can be used to model many diverse structures. The focus of this proposal is on asymptotic results, i.e. the graphs under consideration are large. This often unveils patterns and connections which remain obscure when considering only small graphs. It also allows for the use of powerful techniques such as probabilistic arguments, which have led to spectacular new developments. In particular, my aim is to make decisive progress on central problems in the following 4 areas: (1) Factorizations: Factorizations of graphs can be viewed as partitions of the edges of a graph into simple regular structures. They have a rich history and arise in many different settings, such as edge-colouring problems, decomposition problems and in information theory. They also have applications to finding good tours for the famous Travelling salesman problem. (2) Hamilton cycles: A Hamilton cycle is a cycle which contains all the vertices of the graph. One of the most fundamental problems in Graph Theory/Theoretical Computer Science is to find conditions which guarantee the existence of a Hamilton cycle in a graph. (3) Embeddings of graphs: This is a natural (but difficult) continuation of the previous question where the aim is to embed more general structures than Hamilton cycles - there has been exciting progress here in recent years which has opened up new avenues. (4) Resilience of graphs: In many cases, it is important to know whether a graph `strongly’ possesses some property, i.e. one cannot destroy the property by changing a few edges. The systematic study of this notion is a new and rapidly growing area. I have developed new methods for deep and long-standing problems in these areas which will certainly lead to further applications elsewhere.

818 414 €

Start date: 2012-12-01, End date: 2018-11-30