Suraj Yadav: A^1-connectivity of the moduli stack of vector bundles on a curve

Abstract

Based on joint work with Amit Hogadi, I will talk about \(\mathbb{A}^1\)-connectivity, \(\pi_0^{\mathbb{A}^1}\) , of the moduli stack of vector bundles on a curve and its application to the classification of projective bundles on a curve in motivic homotopy category.

Time permitting, I will also give an overview of the motivic homotopy groups \(\pi_i^{\mathbb{A}^1}\) and their properties over a general base, such as stable connectivity theorems over a general base.