| EPSRC Reference: |
GR/S07148/01 |
| Title: |
Moduli spaces in algebra and homotopy theory |
| Principal Investigator: |
Lazarev, Professor A |
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| Department: |
Mathematics |
| Organisation: |
University of Bristol |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 April 2003 |
Ends: |
31 March 2006 |
Value (£): |
64,331
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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The area of the proposed research in pure mathematics is at the junction of several mathematical disciplines: homotopy theory, homological algebra, number theory and algebraic geometry. Our purpose is to investigate moduli spaces of certain algebraic structures by homotopy-theoretic means. Homotopy theory was originally conceived as the study of the properties of topological spaces which do not change under continuous deformations. However it had soon become clear that the methods and philosophy of homotopy theory extend far beyond this. It is a recent realization that the moduli space problem, or the problem of classification of objects of given type (rings, vector bundles, complex structures etc) is most naturally treated within the framework of homotopy theory.In this project we employ homotopy techniques together with ideas from stable homotopy theory to study moduli spaces of strongly homotopy associative algebras, objects which were initially introduced for the internal purposes of algebraic topology but which recently found numerous impressive applications outside topology. In addition to being an important object of study in its own right this theory oserves as a test model for other moduli problems arising in algebra and geometry.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.bris.ac.uk |