| EPSRC Reference: |
GR/R70200/01 |
| Title: |
Small grants for visiting fellowships: Visit of Professor ALf van der Poorten |
| Principal Investigator: |
Everest, Professor GR |
| Other Investigators: |
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| Researcher Co-Investigators: |
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| Department: |
Mathematics |
| Organisation: |
University of East Anglia |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
18 April 2002 |
Ends: |
17 August 2002 |
Value (£): |
10,129
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| EPSRC Research Topic Classifications: |
| Algebra & Geometry |
Mathematical Analysis |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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| Panel History: |
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Summary on Grant Application Form |
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There are two main areas we hope to pursue. The first is to explore the rich area of overlap between arithmetic and dynamical systems. The particular problems we consider are those associated to the arithmetic of linear recurrence relations. We aim to classify those solutions of a fixed linear recurrence relation which count the periodic points in a dynamical system. This result will include results about known clasical sequences such as Fibonacci, Mersenne and Lucas. The second builds on existing work on a deep connection between Diophantine number theory and ergodic theory: in 1993 Schmidt and Ward showed that the problem of order of mixing for commuting compact group automorphisms on connected groups is intimately connected to the S-unit theorem. The general case involves a positive characteristic version of the S-unit theorem, currently out of reach. The proposal is to examine the mixing problem on zero-dimensional groups from this Diophantine perspective, and to see if van der Poorten's deep knowledge of the subspace theorem will bring some progress in special cases. In particular, recent work of Einsiedler and Ward has pointed at a difficult class of examples with potentially very unexpected order of mixing; these need to be studied using powerful Dlophantine tools.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.uea.ac.uk |