| EPSRC Reference: |
GR/S68491/01 |
| Title: |
Topics in geometric analysis |
| Principal Investigator: |
Singer, Professor M |
| Other Investigators: |
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| Project Partners: |
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| Department: |
Sch of Mathematics |
| Organisation: |
University of Edinburgh |
| Scheme: |
Overseas Travel Grants Pre-FEC |
| Starts: |
01 August 2003 |
Ends: |
31 January 2005 |
Value (£): |
10,129
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| EPSRC Research Topic Classifications: |
| Algebra & Geometry |
Mathematical Analysis |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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Geometric analysis includes the study of (partial) differential operators in geometric settings, i.e. on manifolds, as well as the application of PDE methods to prove geometric results. The objectives in this proposal are of both kinds: what they have in common is the need to study geometric situations which are singular and/or non-compact. In collaboration with Richard Melrose, who is one of the pioneers in this area, I propose to develop new tools and techniques in this general area. The specific research goals are the development of new index theorems for a certain class of non-compact manifolds. With the aid of these new results, we aim to prove the basic conjectures about the L^2 metric on monopole moduli spaces formulated recently by PI and Michael Murray. A more ambitious goal is the development of analytical tools to study singular and nearly-singular projective varieties with possible applications to a more explicit understanding of Kaehler-Einstein metrics on such varieties. The techniques used will combine the Pi's geometric background with his hosts expertise in microlocal analysis. The Department at MIT will provide an extremely stimulating atmosphere for research, and if even more interesting project objectives suggest themselves I would allow myself some latitude in departing from the objectives stated above.
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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 |
| Summary |
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| Date Materialised |
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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.ed.ac.uk |