EPSRC Reference: 
EP/C54076X/1 
Title: 
Geometrical, dynamical and transference principles in nonlinear Diophantine approximation and applications 
Principal Investigator: 
Beresnevich, Professor V 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Mathematics 
Organisation: 
University of York 
Scheme: 
Advanced Fellowship (PreFEC) 
Starts: 
01 October 2005 
Ends: 
30 September 2010 
Value (£): 
271,970

EPSRC Research Topic Classifications: 

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 nonmetrical 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 socalled 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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Potential use in nonacademic contexts 
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Impacts 
Description 
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Summary 

Date Materialised 


Sectors submitted by the Researcher 
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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 