# Jerusalem Mathematics Colloquium

Thursday, 15th January 2004, 4:00 pm
Mathematics Building, Lecture Hall 2

The Jerusalem Mathematics Colloquium is happy to host
the first of the three annual LANDAU LECTURES.

## Professor Jeff Cheeger (Courant Institute, NYU) "Collapsed Manifolds with Bounded Curvature"

Abstract: In this first lecture, we will make the assumption that the full curvature tensor is bounded, say $|R|\leq 1$. The key distinction is between the not too noncollapsed case, in which a sufficiently small ball can be shown to look like a ball in $R^n$, and the sufficiently collapsed case, in which it turns out that $B_{\epsilon(n)}(m)$ looks like an $\epsilon(n)$-tubular neighborhood of the zero section of a vector bundle over some (tiny) nilmanifold. If $B_1(m)$ is sufficiently collapsed for all $m\in M^n$, a coherent collection of nilmanifolds arises, encoding the essential features of the collapsed geometry.

The other two lectures will be
18th January 2004, 3:00 pm, "Four-dimensional Einstein Manifolds"
19th January 2004, 4:00 pm : "Einstein Manifolds in general"

Light refreshments will be served before each lecture

List of talks, 2003-04
List of talks, 2002-03
List of talks, 2001-02
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List of talks, 1998-99
List of talks, 1997-98