From the Donaldson-Uhlenbeck-Yau theorem to stability in mirror symmetry
| dc.contributor.author | Eurenius, Björn | |
| dc.contributor.department | Chalmers tekniska högskola / Institutionen för fysik | sv |
| dc.contributor.examiner | Persson, Daniel | |
| dc.contributor.supervisor | Persson, Daniel | |
| dc.date.accessioned | 2020-01-20T10:18:59Z | |
| dc.date.available | 2020-01-20T10:18:59Z | |
| dc.date.issued | 2019 | sv |
| dc.date.submitted | 2019 | |
| dc.description.abstract | We give an introduction to the mathematical formulation of Yang-Mills theory. In particular we derive the Hermitian-Yang-Mills equation and show that Hermitian-Yang-Mills connections can be described as the zeroes of the corresponding moment map. We then introduce deformed Hermitian- Yang-Mills equations by considering arbitrary moment maps. Furthermore we introduce slope stability of holomorphic vector bundles and show that holomorphic vector bundles have a unique Harder-Narasimhan ltration. We then give a proof of the Donaldson-Uhlenbeck-Yau theorem in the case of algebraic surfaces, which states that there is a one-to-one correspondence between stable bundles and bundles that admit an irreducible Hermitian- Yang-Mills connection. Finally we look at stability in the context of homological mirror symmetry. We discuss Bridgeland stability conditions on the bounded derived category of coherent sheafs Db Coh(M) over a K ahler manifold M and discuss how it connects to the deformed Hermitian-Yang-Mills equation. | sv |
| dc.identifier.coursecode | TIFX05 | sv |
| dc.identifier.uri | https://hdl.handle.net/20.500.12380/300649 | |
| dc.language.iso | eng | sv |
| dc.setspec.uppsok | PhysicsChemistryMaths | |
| dc.subject | Donaldson-Uhlenbeck-Yau theorem | sv |
| dc.subject | deformed Hermitian-Yang-Mills | sv |
| dc.subject | Kobayashi-Hitchin correspondence | sv |
| dc.subject | Mirror symmetry | sv |
| dc.subject | Bridgeland stability | sv |
| dc.title | From the Donaldson-Uhlenbeck-Yau theorem to stability in mirror symmetry | sv |
| dc.type.degree | Examensarbete för masterexamen | sv |
| dc.type.uppsok | H | |
| local.programme | Physics and astronomy (MPPAS), MSc |