Objective Combinatorics forms a challenging and fundamental part of pure mathematics, but is in the happy position of being relatively accessible to a wider audience. One of its most exciting and rapidly developing branches is Extremal Combinatorics, which has a wide range of direct applications both to other areas of mathematics and other academic disciplines. Thus it makes its influence felt indirectly when the theoretical power it brings to these disciplines is in turn used for more practical applications. The proposed project addresses a range of important problems at the frontier of Extremal Combinatorics, principally those motivated by a question of Turan, an open problem that mathematicians have battled with for over sixty years, which has led to many developments in the theory of graphs and hypergraphs. Recently there has been a lot of progress in this area, so it is an exciting topic for future research. The PI has identified some key intermediate goals to pursue for this first objective, and also for a second objective involving various ways to extend the scope of this area, including a rainbow variant that has impressive potential applications in additive number theory. A third area being studied is the theory of set systems with restricted intersections, which has a rich history in combinatorics, and has also found applications to computer science, particular in the theories of complexity and communication. It is also closely connected to the concepts of trace and VC-dimension, which play a central role in many areas of statistics, discrete and computational geometry and learning theory. The PI will co-ordinate a research team of two postdocs and one doctoral student with clearly defined goals that will bring this project to fruition over a five-year period. Fields of science natural sciencesmathematicspure mathematics Programme(s) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Topic(s) ERC-SG-PE1 - ERC Starting Grant - Mathematical foundations Call for proposal ERC-2009-StG See other projects for this call Funding Scheme ERC-SG - ERC Starting Grant Coordinator THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD EU contribution € 512 381,38 Address Wellington square university offices OX1 2JD Oxford United Kingdom See on map Region South East (England) Berkshire, Buckinghamshire and Oxfordshire Oxfordshire Activity type Higher or Secondary Education Establishments Administrative Contact Gill Wells (Ms.) Principal investigator Peter Keevash (Dr.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data Beneficiaries (2) Sort alphabetically Sort by EU Contribution Expand all Collapse all THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD United Kingdom EU contribution € 512 381,38 Address Wellington square university offices OX1 2JD Oxford See on map Region South East (England) Berkshire, Buckinghamshire and Oxfordshire Oxfordshire Activity type Higher or Secondary Education Establishments Administrative Contact Gill Wells (Ms.) Principal investigator Peter Keevash (Dr.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data QUEEN MARY UNIVERSITY OF LONDON Participation ended United Kingdom EU contribution € 267 618,62 Address 327 mile end road E1 4NS London See on map Region London Inner London — East Tower Hamlets Activity type Higher or Secondary Education Establishments Administrative Contact Reuben Almeida (Mr.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data