Courant Differential Geometry and
Topology Seminar
Courant Institute of Mathematical Sciences
251 Mercer Street
New York, NY 10012
Warren Weaver Hall 1314
Tuesday, April 24, 2:00pm
Filling inequalities for nilpotent groups
Robert Young ( University of Chicago )
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.
Note special time and room!!