Because Madison did not offer an algebraic geometry course in the 24fall semester, I invited three professors to help organize a reading course based on [1][2].Â
We met twice a week, once for a talk and once for a discussion of exercises. On behalf of the students, I invited the professor to classroom and assign exercises, and I gave three talks, topics listed below (Sorry but I have not kept my note.)
Week 2: Vector Bundles and Locally free sheaves of finite rank.
Week 5: Open and Closed embedding
Week 6: (Quasi-)Coherent Sheaves, with calculations of ideal sheaves and twisting sheaves
Preparing these talks has helped me improve my presentation skills. Now I know how to prepare and give a one and a half hour talk, and I will continue to actively improve this skill in various seminars and courses.
[1] Hartshorne, R. (1977). Algebraic geometry. Springer.
[2] Vakil, R. (2017). The rising sea: Foundations of algebraic geometry. Unpublished book, available at https://math.stanford.edu/~vakil/216blog/