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| EPSRC Reference: |
GR/T02256/01 |
| Title: |
Families of P-Adic Automorphic Forms, with Applications to Arithmetic and to the Langlands Programme |
| Principal Investigator: |
Professor KM Buzzard |
| Other Investigators: |
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| Researcher Co-investigator: |
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| Project Partner: |
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| Department: |
Mathematics |
| Organisation: |
Imperial College London |
| Scheme: |
Advanced Fellowship |
| Starts: |
01 October 2004 |
Ends: |
31 March 2010 |
Value (£): |
256,907
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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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12 Mar 2004
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Maths Fellowships Sifting Panel 2004
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Deferred
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22 Apr 2004
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Mathematics Advanced Fellowships Interview panel
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Deferred
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Summary |
In the 1970s, Langlands outlined a profound series of conjectures and ideas which have since
become known as "the Langlands philosophy". These conjectures unified various aspects of number theory and representation theory, and still have a profound influence on much of modern research in both areas. Langlands' conjectures related representations of Galois groups and related groups to automorphic forms, objects which are typically defined analytically. On the other hand, in many cases one can define automorphic forms, or certain classes of automorphic forms, using algebraic geometry or combinatorics. Langlands' conjectures explain many phenomena in this area, but they do not seem to shed too much light on the "extra" p-adic objects that may show up in this more algebraic setting (for example,
modular forms of non-integral weight studied by Katz and Hida). On the other hand, there has also been much recent progress in the p-adic representation theory of Galois groups. People nowadays would like to begin to relate arithmetic progress in both areas via some kind of "p-adic Langlands philosophy", and formulating such a philosophy is at the heart of my proposal.
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| Final Report Summary |
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No final report summary is available for this grant.
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| Further Information: |
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| Organisation Website: |
http://www.ic.ac.uk |
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