Details of Grant 

EPSRC Reference:	EP/K016687/1
Title:	Topology, Geometry and Laplacians of Simplicial Complexes
Principal Investigator:	Peyerimhoff, Professor N
Other Investigators:	Ivrissimtzis, Dr I Dantchev, Dr SS Vdovina, Dr A
Researcher Co-Investigators:	Dr S Liu
Project Partners:
Department:	Mathematical Sciences
Organisation:	Durham, University of
Scheme:	Standard Research
Starts:	01 October 2013	Ends:	09 December 2016	Value (£):	395,679
EPSRC Research Topic Classifications:	Algebra & Geometry Logic & Combinatorics
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
Related Grants:
Panel History:	Panel Date Panel Name Outcome 13 Mar 2013 Mathematics Prioritisation Panel Meeting March 2013 Announced
Summary on Grant Application Form
Simplicial complexes are natural abstract mathematical objects which play a prominent role in several fields of mathematics. They appear as triangulations of surfaces or more general higher dimensional spaces, which are useful in topology for the computation of invariants like the Euler characteristic. Other important examples of simplicial complexes, in connection with geometric group theory, are buildings. They were first introduced by Jacques Tits in his work on Klein's Erlangen program and provide a very successful geometric approach to group theory. Being combinatorial objects, simplicial complexes can serve as simplified models of smooth geometric spaces. Their combinatorial nature allows explicit computations of their fundamental groups. Fundamental groups are a basic algebraic tool to describe the equivalence of closed paths under continuous deformations. In this project, we aim to obtain a better understanding of the fundamental groups of simplicial complexes and their properties. Another attractive property of simplicial complexes is that they can be endowed with additional geometric structures and become gateways to a much richer world than the classical surfaces and their generalisation to higher dimensions (manifolds). In this project, we aim is to generalize known geometric concepts of curvature into this richer world. Another consequence of the simplicity and versatility of simplicial complexes is their wide use as geometric representations in the fields of industrial design and medical imaging. The better understanding of their mathematical properties will lead to improved processing algorithms that can be used in these applications.
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: