## EVENT DETAILS AND ABSTRACT

**Workshop on Ricci Curvature**
**Title:** Quantitative nilpotent structure and epsilon-regularity on collapsed manifolds with Ricci curvature bounds

**Speaker:** Ruobing Zhang

**Speaker Info:** Princeton

**Brief Description:**

**Special Note**:

**Abstract:**

In this talk we discuss the ε-regularity theorems for
Einstein manifolds and more generally manifolds with just bounded Ricci
curvature, in the collapsed setting. A key tool in the regularity theory of
noncollapsed Einstein manifolds is the following: If a bigger geodesic
ball on an Einstein manifold is sufficiently Gromov-Hausdorff-close to a
ball on the Euclidean space of the same dimension, then in fact the
curvature on a smaller ball is uniformly bounded. No such results are
known in the collapsed setting, and in fact it is easy to see without more
such results are false. It turns out that the failure of such an estimate
is related to topology. Our main theorem is that for the above setting in
the collapsed context, either the curvature is bounded, or the local
nilpotent rank drops. There are generalizations of this result to bounded
Ricci curvature and even just lower Ricci curvature. This is a joint work
with Aaron Naber.

**Date:** Sunday, May 31, 2015

**Time:** 12:00pm

**Where:** Swift 107

**Contact Person:** Valentino Tosatti

**Contact email:** tosatti@math.northwestern.edu

**Contact Phone:**

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