Day 1: Introduction, Grassmannians, basic properties, Plueker embedding, Schubert varieties Lecture 1
Day 2-3: Grassmannians, local theory, their cohomology, Pieri and Giambelli rules Lecture 2
Day 3-4: Grassmannians, geometric Littlewood-Richardson Better notes For this lecture start with page 20 in these notes.
Day 4-5: Grassmannians, various aspects of their geometry, rigidity of classes, dual varieties Lecture 4
Day 6-7: Isotropic Grassmannians, their basic geometry, Schubert varieties, the restriction problem Lecture 5
Day 8: Flag varieties, Schubert classes, cohomology, the quantum cohomology of Grassmannians
No longer to be covered: Exceptional homogeneous varieties, rigidity, the Tits transform as a way of understanding the Cayley plane and the Freudenthal variety.
You can find additional exercises here
These lectures are generously supported by the Polish Financial Means for Science 2012--2014 under the research project "Uklady linii na zespolonych rozmaitosciach kontaktowych oraz uogolnienia''