Anand Sawant

We will describe the $\mathbb{A}^1$-fundamental sheaf of groups of a split reductive group and discuss some consequences.  The key tool in the computation is the use of the notion of cellular $\mathbb{A}^1$-homology, which will be introduced in the talk.  We will also discuss how our results uniformly explain the classical results of Matsumoto, Suslin and Brylinski-Deligne about universal central extensions of algebraic groups.  The talk is based on joint work with Fabien Morel.