Details of Grant 

EPSRC Reference:	EP/I020276/1
Title:	Groups acting on Asymptotically CAT(0) spaces
Principal Investigator:	Kar, Dr A
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department:	Mathematical Institute
Organisation:	University of Oxford
Scheme:	Postdoc Research Fellowship
Starts:	01 October 2011	Ends:	30 September 2014	Value (£):	212,208
EPSRC Research Topic Classifications:	Algebra & Geometry
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
Geometric group theory is the mathematical tool for studying symmetry. This is achieved by investigating groups via their actions on geometric spaces. A fundamental class of objects studied by geometric group theorists are manifolds or varieties which are solutions sets to collections of equations. A collection of equations or parameters could arise naturally in different areas of mathematics, of science and in economics. Hence research in geometric group theory is of paramount importance. In this proposal we are interested in groups acting on trees, a theory that was initiated by Bass and Serre and has profound influence on the splittings of groups as amalgamated free products and HNN extensions. If a group splits, then one can decompose it into smaller, more manageable pieces. The fundamental group links group theory to geometry and topology. Splitting the fundamental group of a manifold holds the key in some cases to splitting the manifold itself into smaller better-understood sub-manifolds. This is related to important conjectures in mathematics like the virtual Haken conjecture. We hope that the work arising from this proposal will enlighten us on the phenomenon of splittings of groups and manifolds. A second theme of the project is to exhibit the richness of the class of what we call asymptotically CAT(0) spaces which heuristically are metric spaces appearing to have non-positive curvature when viewed from increasingly distant observation points. Trees and hyperbolic spaces are natural examples. We hope to construct examples of asymptotically CAT(0) graphs which not hyperbolic in the sense of Gromov. This is related to a question of Erdos held in esteem among computer scientists and graph theorists. Evidently a resolution of Erdos' question will allow us to solve geometric problems algorithmically on computer.
Key Findings
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
Potential use in non-academic contexts
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
Impacts
Description This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk Summary Date Materialised
Sectors submitted by the Researcher
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
Project URL:
Further Information:
Organisation Website:	http://www.ox.ac.uk