The Isoperimetric Inequality for SL(n, Z)

September 8 to September 12, 2008

at the

American Institute of Mathematics, San Jose, California

organized by

Nathan Broaddus, Tim Riley, and Kevin Wortman

Original Announcement

This workshop has the goal of determining the isoperimetric function of SL(n,Z).

Isoperimetric functions (or Dehn functions) are a measure of the efficiency of solving the word problem in a finitely presented group. Also they record the minimal areas of discs spanning loops in spaces associated to such groups. So, from both combinatorial and geometric viewpoints, they are vital to understanding a group. Unfortunately, despite receiving substantial attention, isoperimetric inequalities remain ill-understood for some groups of fundamental interest--the groups SL(n,Z) being the outstanding examples.

We intend to give the background to this problem and to attack it by examining the diverse known approaches--via differential or combinatorial geometry in symmetric spaces, buildings etc..

Related questions, such as concerning isodiametric functions, asymptotic cones, higher dimensional isoperimetric functions, other arithmetic groups, Aut(Fn) and Out(Fn), will also receive attention.

We hope this workshop will lead to improved understanding of the geometry of many important groups and the nature of isoperimetric functions.

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

Papers arising from the workshop:

The Dehn function of SL(n;Z)
by  Robert Young
A polynomial isoperimetric inequality for SL(n,Z)
by  Robert Young