| EPSRC Reference: |
EP/I03322X/1 |
| Title: |
Gauge Theory and Complex Geometry |
| Principal Investigator: |
Bielawski, Professor R |
| Other Investigators: |
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| Department: |
Pure Mathematics |
| Organisation: |
University of Leeds |
| Scheme: |
Standard Research |
| Starts: |
04 July 2011 |
Ends: |
03 October 2011 |
Value (£): |
23,903
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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The interaction between gauge theory and complex geometry, which goes back to 1970s, has resulted in some of the most stunning achievements in both mathematics and in theoretical physics. These include twistor-theoretic construction of instantons on the 4-sphere, Donaldson's breakthrough results for algebraic surfaces, and the Hitchin-Kobayashi correspondence between stable holomorphic bundles and anti-self-dual connections. Both fields continue to influence each other and recent years have yielded a host of new developements and applications to new topics in both areas. Among these developements are applications of gauge-theoretic methods to non-Kaehlerian surfaces; gauge theory over complex manifolds with anti-holomorphic involution (so called orientifolds) leading to deep conjectures by C. Vafa and collaborators; the Donaldson-Thomas invariants, which allow application of gauge theoretic methods to higher-dimensional algebraic manifolds; and the geometry of the moduli spaces of Higgs bundles with their increasing relevance to the geometric Langlands programme.
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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.leeds.ac.uk |