EPSRC Reference: 
EP/I019588/1 
Title: 
The arithmetic of padic automorphic forms and Galois representations 
Principal Investigator: 
Newton, Professor J 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

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

EPSRC Research Topic Classifications: 

EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 
Panel Date  Panel Name  Outcome 
15 Feb 2011

PDRF Maths Interview Panel

Announced

01 Feb 2011

PDRF Maths Sift Panel

Announced


Summary on Grant Application Form 
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 SatoTate.In recent years number theorists have been to develop an extension of the Langlands programme which seeks to understand the finer padic structure of automorphic forms and Galois representations (particularly the way they move in padic families). This proposal focuses on developing this `padic Langlands programme', which is currently only understood in special cases.Specific aims of the proposal include proving some cases of padic Langlands functoriality, allowing one to move between padic automorphic forms on different groups, by studying the arithmetic of Shimura varieties for unitary groups. Secondly, studying padic 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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Further Information: 

Organisation Website: 
http://www.cam.ac.uk 