at the

American Institute of Mathematics, Palo Alto, California

organized by

Nathan Broaddus, Tim Riley, and Kevin Wortman

This workshop, sponsored by
AIM and the
NSF,
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

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

The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

The deadline to apply for support to participate in this workshop has passed.

For more information email *workshops@aimath.org*

Plain text announcement or brief announcement.

Go to the
American Institute of Mathematics.

Go to the
list of upcoming workshops.