| EPSRC Reference: |
EP/M029719/1 |
| Title: |
The local Langlands correspondence in families |
| Principal Investigator: |
Helm, Dr D |
| Other Investigators: |
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| Researcher Co-Investigators: |
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| Department: |
Mathematics |
| Organisation: |
Imperial College London |
| Scheme: |
Standard Research |
| Starts: |
01 November 2015 |
Ends: |
31 October 2018 |
Value (£): |
315,611
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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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16 Jun 2015
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EPSRC Mathematics Prioritisation Panel June 2015
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Announced
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Summary on Grant Application Form |
The Langlands program is a series of far-reaching conjectures, dating back to the 1970s, that relate such widely separate branches of mathematics as number theory, representation theory, harmonic analysis, and mathematical physics. Central to the Langlands program is the local Langlands correspondence, which relates admissible representations of p-adic groups (objects from harmonic analysis)
to Galois representations (objects from number theory). It has recently become clear that in order to properly understand this correspondence, we should consider not just single examples of objects on both sides of the correspondence, but whole families of such objects, that vary as one varies certain parameters.
This leads naturally to the following question: if one varies the objects on one side of the correspondence, how do the objects on the other side of the correspondence change? The proposed research seeks to develop a version of the local Langlands correspondence that addresses this question. Moreover, the answer to this questions should have extensive applications within the Langlands program, particularly to Emerton's "p-adic global Langlands correspondence". We seek to explore these applications and deduce new results in the Langlands program via these techniques.
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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.imperial.ac.uk |