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Extremal Combinatorics

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.

Field of science

  • /natural sciences/mathematics/pure mathematics

Call for proposal

ERC-2009-StG
See other projects for this call

Funding Scheme

ERC-SG - ERC Starting Grant

Host institution

THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
Address
Wellington Square University Offices
OX1 2JD Oxford
United Kingdom
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 512 381,38
Principal investigator
Peter Keevash (Dr.)
Administrative Contact
Gill Wells (Ms.)

Beneficiaries (2)

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
Activity type
Higher or Secondary Education Establishments
Principal investigator
Peter Keevash (Dr.)
Administrative Contact
Gill Wells (Ms.)
QUEEN MARY UNIVERSITY OF LONDON

Participation ended

United Kingdom
EU contribution
€ 267 618,62
Address
327 Mile End Road
E1 4NS London
Activity type
Higher or Secondary Education Establishments
Administrative Contact
Reuben Almeida (Mr.)