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EP/K016687/1 - Topology, Geometry and Laplacians of Simplicial Complexes

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Dr N Peyerimhoff EP/K016687/1 - Topology, Geometry and Laplacians of Simplicial Complexes

Principal Investigator - Mathematical Sciences, Durham University

Other Investigators

Dr SS Dantchev, Co InvestigatorDr SS Dantchev

Dr I Ivrissimtzis, Co InvestigatorDr I Ivrissimtzis

Dr A Vdovina, Co InvestigatorDr A Vdovina

Scheme

Standard Research

Research Areas

Algebra Algebra

Geometry & Topology Geometry & Topology

Logic and Combinatorics Logic and Combinatorics

Start Date

06/2013

End Date

05/2016

Value

£395,679

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Grant Description

Summary and Description of the grant

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.


Structured Data / Microdata


Grant Event Details:
Name: Topology, Geometry and Laplacians of Simplicial Complexes - EP/K016687/1
Start Date: 2013-06-01T00:00:00+00:00
End Date: 2016-05-31T00:00:00+00:00

Organization: Durham University

Description: 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 computati ...