**Amit Hogadi**

TIFR

March 22, 2012

**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.