# Geometric Analysis and Topology Seminar

#### Filling Inequalities for Nilpotent Groups

**Speaker:**
Robert Young, U Chicago

**Location:**
Warren Weaver Hall 1314

**Date:**
Tuesday, April 24, 2007, 2 p.m.

**Synopsis:**

A homogeneous nilpotent Lie group has a scaling automorphism which acts as a homothety on a leftinvariant subriemannian metric. Many upper bounds for the Dehn function of such a group depend on filling curves with discs which grow slowly when scaled. Gromov developed a method which uses microflexibility to construct a compact family of such discs and uses the scaling automorphism to connect the discs into fillings of curves; this provides a bound on the Dehn function of the group and a method for constructing fillings satisfying certain tangency conditions.

I will extend this technique to higher dimensional fillings and show that in the case that the Lie group contains a lattice, it suffices to construct finitely many discs. I will use this to construct the first examples of nilpotent groups with arbitrarily large nilpotency class and quadratic Dehn functions.