In-Person Talk 

In this talk, we will discuss local topology of a Ricci limit space $(X,p)$, which is the pointed Gromov-Hausdorff limit of a sequence of complete $n$-manifolds with a uniform Ricci curvature lower bound. I will show that $(X,p)$ is semi-locally simply connected, that is, for any point $x \in X$, we can find a small ball $B_r(x)$ such that any loop in $B_r(x)$ is contractible in $X$. We will also discuss a slice theorem for pseudo-group actions on the Ricci limit space and how to use this slice theorem to construct a homotopy map on the limit space. Partial of this material is joint work with Jiayin Pan.