Details of Grant 

EPSRC Reference:	GR/T02256/01
Title:	Families of P-Adic Automorphic Forms, with Applications to Arithmetic and to the Langlands Programme
Principal Investigator:	Buzzard, Professor K
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department:	Mathematics
Organisation:	Imperial College London
Scheme:	Advanced Fellowship (Pre-FEC)
Starts:	01 October 2004	Ends:	31 March 2010	Value (£):	256,907
EPSRC Research Topic Classifications:	Algebra & Geometry
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
Related Grants:
Panel History:	Panel Date Panel Name Outcome 22 Apr 2004 Mathematics Advanced Fellowships Interview panel Deferred 12 Mar 2004 Maths Fellowships Sifting Panel 2004 Deferred
Summary on Grant Application Form
In the 1970s, Langlands outlined a profound series of conjectures and ideas which have sincebecome 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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Organisation Website:	http://www.imperial.ac.uk