| EPSRC Reference: |
EP/I019588/1 |
| Title: |
The arithmetic of p-adic automorphic forms and Galois representations |
| Principal Investigator: |
Newton, Professor J |
| Other Investigators: |
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| Researcher Co-Investigators: |
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| Project Partners: |
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| Department: |
Pure Maths and Mathematical Statistics |
| Organisation: |
University of Cambridge |
| Scheme: |
Postdoc Research Fellowship |
| Starts: |
01 October 2011 |
Ends: |
30 September 2014 |
Value (£): |
247,241
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| EPSRC Research Topic Classifications: |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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| Related Grants: |
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| Panel History: |
| Panel Date | Panel Name | Outcome |
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15 Feb 2011
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PDRF Maths Interview Panel
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Announced
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01 Feb 2011
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PDRF Maths Sift Panel
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Announced
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Summary on Grant Application Form |
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One of the fundamental problems in number theory is to understand linear representations of the Galois groups of number fields. These encode structure and symmetries of the number fields (for example the rational numbers).The Langlands programme seeks to study these Galois representations using automorphic forms - these are special kinds of analytic functions which are conjecturally (and sometimes provably) related to Galois representations. Initiated in the 1970s, the work of Langlands and others has been extremely influential, playing a crucial part in Wiles and Taylor's celebrated proof of Fermat's last theorem, as well as more recent results on conjectures of Serre and Sato-Tate.In recent years number theorists have been to develop an extension of the Langlands programme which seeks to understand the finer p-adic structure of automorphic forms and Galois representations (particularly the way they move in p-adic families). This proposal focuses on developing this `p-adic Langlands programme', which is currently only understood in special cases.Specific aims of the proposal include proving some cases of p-adic Langlands functoriality, allowing one to move between p-adic automorphic forms on different groups, by studying the arithmetic of Shimura varieties for unitary groups. Secondly, studying p-adic Banach space representations of GL_2(K), where K is a finite extension of Q_p, using tools from arithmetic geometry and the completed cohomology of Shimura curves.
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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.cam.ac.uk |