## Differential geometry

### Prof. Boris Dubrovin

Content:

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