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Seminar on Gauge Theory SemesterSoSe 2018 Lecturer Bernd Ammann, Raphael Zentner Type of course (Veranstaltungsart) Seminar Contents The subjects of the seminar are Donaldson's instanton theory and Seiberg-Witten theory. Both theories associate invariants to closed 4-manifolds. These invariants yield obstructions against positive scalar curvature metrics, even in situations when index theoretical methods fail. For example, in dimension 4 there exist simply-connected closed non-spin manifolds without metrics of positive scalar curvature, which is amazing, as there are no such manifolds in any other dimension. Donaldson's instanton theory uses moduli spaces of connections with self-dual curvature. Such connections yield solutions to the Yang-Mills equations, which can be considered as a Riemannian analogue of the vacuum Maxwell equations on 3+1-dimensional spacetime. An infinite-dimensional group, the "gauge group" acts on the space of solutions, but the quotient of the space of solutions by the gauge group is a finite-dimensional manifold, which provides these invariants. Seiberg-Witten theory is structurally similar, but uses spinors instead of connections. The seminar will provide the foundations of these two gauge theories, and thus it will provide the knowledge to understand the main topics in summer school and a conference of the CRC Higher Invariants in July 2018. There also examples homeomorphic manifolds Literature
Recommended previous knowledge Profound knowledge about manifolds and riemannian metrics Time/Date Monday 16-18 Location M103 Course homepage http://www.mathematik.uni-regensburg.de/ammann/lehre/2018s_gauge (Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern) Registration
BSem, MV, MSem ECTS Siehe Modulkatalog. MV und Nebenfach: 4,5 LP bei Studienbeginn ab WS 15/16, 6 LP bei Studienbeginn vor WS 15/16 |