**NOTE NEW TIME: 3:00 pm**
Siddharth Mathur, Mittag-Leffler Institute
"Global structure results in algebraic geometry"
It is a classical result that any smooth manifold can be embedded into Euclidean space. However, the analogous statement is false in the algebraic setting. Indeed, there are many varieties which cannot be embedded in Euclidean (or even projective) space!
In this talk we will discuss a way to salvage this deficiency using algebraic vector bundles. Indeed, a result of Totaro explains why the existence of special vector bundles implies a higher-rank analogue of the embeddability results above. We will then explain why the Brauer group, a repository of arithmetic and geometric data, can help achieve new global structure results in this direction.