Differential geometry

Prof. Boris Dubrovin


  1. Basic Riemannian and pseudo-Riemannian geometry.
  2. Complex geometry (especially Riemann surfaces).
  3. Lie groups.
  4. Theory of geodesics (with some sketches of Morse theory).
  5. Geometry vs. topology (application of ideas of Riemannian geometry to the problem of classification of smooth manifold).
  6. Homotopic topology (with application to the computation of some homotopy groups of spheres).
  7. Morse theory (some applications to mirror symmetry).