The Isoperimetric Inequality for SL(n, Z)

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 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.

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

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