Roman Sauer

The waist inequality for the sphere by Gromov is wonderful result of geometric measure theory. Formulated appropriately for families of spaces, 
a (uniform) waist inequality for a family of Riemannian manifolds is the Riemannian analog of higher dimensional expanders. We formulate a conjectural picture 
for locally symmetric spaces. Finally, we show that the Kazhdan property alone gives rise not only to expanders, which is classical, but also to 2-dimensional expanders. 
An extra dimension for free. We will assume no prior knowledge of expanders and property T. 

This is joint work with Uri Bader.