- Monday. Schubert calculus.
- Wednesday. Schubert calculus.
- Friday. No class (thesis parade).
HW 12 due by noon Thursday, May 16HW 12 (fancy solution template, plain solution template)
- Examples of manifolds, especially projective space; definition of the category of manifolds.
- Tangent space: three equivalent characterizations.
- Multilinear algebra.
- Multilinear algebra on manifolds. Orientations.
- Integration; manifolds with boundary.
- Tangent space for manifolds with boundary; the Cartan derivative; Stokes’ theorem.
- De Rham cohomology; homotopy invariance.
- Mayer-Vietoris, vector fields on spheres, scalar products.
- Semi-Riemannian manifolds; the Hodge \(*\)-operator. Poincaré duality.
- Toric varieties: basic constructions, cohomology, homogeneous coordinates.
- Embeddings of toric varieties. Grassmannians.
- Plücker embedding. Schubert varieties.
- The Schubert calculus.