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EP/H002383/2 - Tools of Applied Algebraic Topology

Research Perspectives grant details from EPSRC portfolio

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Professor M Farber EP/H002383/2 - Tools of Applied Algebraic Topology

Principal Investigator - Mathematics, University of Warwick

Scheme

Standard Research

Research Areas

Geometry & Topology Geometry & Topology

Logic and Combinatorics Logic and Combinatorics

Statistics and Applied Probability Statistics and Applied Probability

Start Date

10/2011

End Date

02/2014

Value

£225,458

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Grant Description

Summary and Description of the grant

The project develops tools of algebraic topology which are relevant to various applications. We will study topological aspects of the problem of building motion planning algorithms and homotopy invariants of topological spaces which reflect the complexity of these algorithms. These invariants were computed previously for some interesting examples, and in this research we plan to resolve several remaining important challenges and also adopt the results for a number of applications. We plan to express the topological complexity TC(X) for aspherical spaces X in terms of the fundamental group of the space X hoping to find new connections with homological algebra and geometric group theory. We plan to explore further the connection between the motion planning problem and the classical problems of geometric topology (embeddings and immersions of manifolds) in the case of lens spaces hoping to find generalizations of recent results concerning real projective spaces. We also plan to study a modification of the theory of motion planning algorithms and their topological complexity relevant to the theory of concurrent computation. In this research we will also study new problems of a mixed topological - probabilistic character dealing with topological spaces depending on a large number of random parameters. The main motivation for studying such spaces comes from engineering applications involving large mechanical systems; their configuration spaces are major examples of such random topological spaces . In our previous work we studied in detail configuration spaces of mechanical linkages with large number of links and with random bar lengths. In this research we plan to investigate other mechanisms producing random topological spaces, such as configuration spaces of particles of random size, and various models based on random graphs.

Structured Data / Microdata


Grant Event Details:
Name: Tools of Applied Algebraic Topology - EP/H002383/2
Start Date: 2011-10-01T00:00:00+00:00
End Date: 2014-02-28T00:00:00+00:00

Organization: University of Warwick

Description: The project develops tools of algebraic topology which are relevant to various applications. We will study topological aspects of the problem of building motion planning algorithms and homotopy invariants of topological spaces which reflect the complexity ...