#
The Isoperimetric Inequality for SL(n, Z)

September 8 to September 12, 2008
at the

American Institute of Mathematics,
Palo Alto, 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(F*_{n}) and *Out(F*_{n}), 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.