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Details of Grant 

EPSRC Reference: EP/L005190/1
Title: Geometrisation of p-adic representations of p-adic Lie groups
Principal Investigator: Ardakov, Professor K
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department: Mathematical Institute
Organisation: University of Oxford
Scheme: EPSRC Fellowship
Starts: 01 October 2013 Ends: 02 August 2019 Value (£): 787,972
EPSRC Research Topic Classifications:
Algebra & Geometry
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:
Panel DatePanel NameOutcome
24 Jul 2013 EPSRC Mathematics Fellowships Interviews - July 2013 Announced
12 Jun 2013 Mathematics Prioritisation Panel Meeting June 2013 Announced
Summary on Grant Application Form
The proposed research is in Pure Mathematics, more precisely, in an area of intersection of Algebraic Number Theory and Representation Theory. One of the main goals of the first subject is to solve Diophantine problems that ask for whole number solutions to polynomial equations in several variables. A very famous example of such a Diophantine problem is due to the French mathematician Fermat, and asks whether it is possible for the sum of two integer n-th powers to be again the n-th power of an integer. When the parameter n is equal to two, it has been known since ancient times that there are infinitely many solutions to this problem, such as 9 + 16 = 25 and 25 + 144 = 169. Fermat guessed way back in the seventeenth century that his problem has no interesting solutions whatsoever for any higher value of n, but a rigorous proof of this guess, the so-called Fermat's Last Theorem, was only obtained around 20 years ago by the British mathematician Andrew Wiles. The second subject, Representation Theory, tries to determine all the possible ways in which symmetries can occur in nature, and has numerous applications in several neighbouring academic disciplines such as Crystallography and Theoretical Physics. A typical problem in Representation Theory asks for the classification of the basic building blocks, or atoms, of the theory --- known as the irreducible representations. To mention an example: according to the Standard Model of Theoretical Physics, nearly everything around us in the visible universe is composed of certain elementary particles called Quarks. The classification and behaviour of these quarks is in turn explained by the classification and behaviour of the irreducible representations of the three-dimensional special unitary group SU(3). The proposed research will develop new geometric tools and methods in order to classify the irreducible representations in a particular sub-field of Representation Theory. This classification project would then be used to build a conceptual bridge called the p-adic local Langlands correspondence between Algebraic Number Theory and Representation Theory, which would in turn be used to make progress in both areas by transferring information from one to the other.

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