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Lectures [Thursdays, 13:00-15:00]

  • Lecture 1, 10.01.2019: Submanifolds of Euclidean space, the Implicit Function Theorem, abstract manifolds.
  • Lecture 2, 17.01.2019: Tangent vectors and the tangent bundle, vector bundles.
  • Lecture 3, 24.01.2019: Vector fields and flows, Lie derivative, the Frobenius Theorem. (Lecture by Alexander Shapiro.)
  • Lecture 4, 31.01.2019: Differential forms, integration on manifolds.
  • Lecture 5, 07.02.2019: de Rham cohomology.
  • Lecture 6, 14.02.2019: Riemannian metrics, connections, the Levi-Civita connection. (Lecture by Andrea Appel.)
  • Lecture 7, 21.02.2019: Geodesics, the exponential map. (Lecture by Sjoerd Beentjes.)
  • Lecture 8, 28.02.2019: Curvature and integrability, Riemannian curvature, spaces with constant curvature.
  • Lecture 9, 07.03.2019: Geometry of hypersurfaces of Euclidean space, the Gauss-Bonnet Theorem.
  • Lecture 10, 14.03.2019: Curvature and topology: Chern-Weil theory, second variation arguments, the Bochner technique. 


This module is assessed in two assignments.


Working knowledge of metric spaces, linear algebra, group theory, vector calculus, topological spaces, the fundamental group, homology. 


The Team