# Colloquium abstracts

Fundamental group of varieties in positive characteristic:  The fundamental group is one of the most basic topological invariant of a space. In this talk we will discuss various notions of fundamental group, like Grothendieck's etale fundamental group, Nori's fundamental group scheme, the $S$-fundamental group scheme, etc. which make sense for varieties over arbitrary fields. We will discuss properties like birational invariance of the $S$-fundamental group scheme (joint work with Vikram Mehta). We will also see introduce a new notion of fundamental group called '$\infty$-stratified fundamental group scheme' (joint work with H\'el\`ene Esnault) and its relation with other existing notions of fundamental group.