240157 Masterkurs I Globale Analysis (V) (WiSe 2020/2021)
Contents, comment
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1. Analysis auf Mannigfaltigkeiten
- Garben
- Differentialoperatoren
- Integration
- Kohomologie2. Zusammenhänge
- Hauptfaserbündel und Vektorbündel
- Krümmung
- Chern-Weil-Theorie
- Strukturen auf Mannigfaltigkeiten: (Semi-)riemannsch, komplex, symplektisch
- Dirac-Operator3. Elliptische Operatoren
- Regularität
- geometrische Differentialoperatoren
- VerschwindungssätzeEin Link zur Vorlesung findet sich im Lernraum.
Requirements for participation, required level
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Kenntniss einiger grundlegender Begriffe aus Algebra, Analysis und Topologie sind empfohlen.
Algebra: Tensorprodukte und multilineare Abbildungen, Gruppen, Algebren, exakte Sequenzen.
Analysis: Maße, gleichmäßige Stetigkeit, Sätze über implizite und inverse Funktionen, Existenz und Eindeutigkeit von Lösungen gewöhnlicher Differentialgleichungen, Hilbert-Räume
Topologie: Kompaktheit und Zusammenhang, Überlagerungen, FundamentalgruppeKenntnisse aus der elementaren Differentialgeometrie (Kurven und Flächen) sind hilfreich.
Bibliography
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- I. Agricola und T. Friedrich: Globale Analysis
- S. Ramanan: Global Calculus
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- Monday, July 27, 2020
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- Thursday, September 24, 2020
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- Thursday, September 24, 2020
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- lecture (V) / 4
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- Faculty of Mathematics
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