Details of Grant 

EPSRC Reference:	EP/C54076X/1
Title:	Geometrical, dynamical and transference principles in non-linear Diophantine approximation and applications
Principal Investigator:	Beresnevich, Professor V
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department:	Mathematics
Organisation:	University of York
Scheme:	Advanced Fellowship (Pre-FEC)
Starts:	01 October 2005	Ends:	30 September 2010	Value (£):	271,970
EPSRC Research Topic Classifications:	Algebra & Geometry
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
Related Grants:
Panel History:	Panel Date Panel Name Outcome 18 Apr 2005 Mathematical Sciences ARF interviews Deferred 14 Mar 2005 Maths Fellowships 2005 Sifting Panel Deferred
Summary on Grant Application Form
The research is mainly devoted to Diophantine approximation, a branch of Number Theory, which can be described as a more quantitative and general analysis of the property that any real number is arbitrarily close to rational numbers. The metrical theory of Diophantine approximation specializes on the study of typical Diophantine properties of numbers. It is also related to more traditional non-metrical problems in Number theory.When the approximated numbers are confined by some relations, the corresponding questions become much harder. For a long time only classical problems concerning relations given by integral polynomials have been significantly developed. However, recent dramatic progress, which includes a breakthrough of G. Margulis and D. Kleinbock, has brought new methods and answered some principle questions in metrical theory of Diophantine approximation concerning general relations. Further deeper and more complicated problems regarding the so-called simultaneous form of Diophantine approximation and Hausdorff measures of related sets have been brought to the forefront. They include, for example, a generalisation of a problem of W.M. Schmidt and A. Baker for arbitrary resonably defined surfaces in multidimensional spaces. Such questions constitute the main body of the proposed research.The theory of Diophantine approximation is closely related to other subjects such as fractal geometry, the geometry of numbers, uniform distribution, which would also benefit from the proposed research. Diophantine approximation is also linked to mathematical physics and dynamical systems via the phenomenon of resonance. This phenomenon is associated with equations in integers and is therefore related to Diophantine approximation. The classical example is the question of staility of the motion of the Solar System. The proposed research is also be concerned with such applications.
Key Findings
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Project URL:	http://gow.epsrc.ac.uk/ViewGrant.aspx?GrantRef=EP/C54076X/1
Further Information:
Organisation Website:	http://www.york.ac.uk