Aditya Sarma Phukon, Temple University
This is the first of two talks based on a paper on normal bundles on rational curves in Grassmannians by Coskun, Larson and Vogt. We shall introduce vector bundles on a manifold as locally free sheaves and talk about short exact sequences of sheaves. Thereafter we will talk about line bundles and then prove Birkhoff-Grothendieck's theorem which says that every vector bundle on $\mathbb{P}^1$ splits into line bundles. We then define a j-balanced vector bundle and present three very simple lemmas about these bundles. Finally, we shall introduce rational curves and thereafter Grassmannians and state a few lemmas about normal bundles. These surprisingly simple tools will be used to finally prove the main theorem in the next talk.