Details of Grant 

EPSRC Reference:	EP/G024979/1
Title:	Non-commutative fundamental groups in Diophantine geometry
Principal Investigator:	Kim, Professor M
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department:	Mathematics
Organisation:	UCL
Scheme:	Standard Research
Starts:	31 August 2009	Ends:	01 October 2011	Value (£):	358,962
EPSRC Research Topic Classifications:	Algebra & Geometry
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
Related Grants:
Panel History:	Panel Date Panel Name Outcome 03 Dec 2008 Mathematics Prioritisation Panel Announced
Summary on Grant Application Form
This proposal is concerned primarily with Diophantine equations in two variables, i.e., polynomial relations with integers coefficients for which one seeks to understand the collection of integer solutions. The history of such investigations reaches back to the tradition of Greek mathematics, while the twentieth century has seen spectacular applications of abstract modern machinery to the resolution of difficult old questions, such as Wiles' proof of Fermat's last theorem. The investigator proposes a new approach to studying these classical problems by incorporating fundamental ideas of topology and geometry that go beyond the principal developments of the twentieth century in that the relevant structures are, in the main, non-commutative and non-linear. An eventual goal is to construct methods for effectively resolving Diophantine equations in two-variables.
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