The January 1994 Workshop at the Geometry Center

About twenty people, each experienced in group theoretic or algebraic programming attended the workshop. The participants specialize in different areas of group theory, topology, and computer science and were not all acquainted. The original plan was to have each person introduce himself or herself by giving a short talk or computer demonstration. Three five minute talks were scheduled for eleven in the morning and one fifteen minute computer demo at four in the afternoon. The rest of the time was left free for informal interaction. The original plan was adhered to except that the talks and demos tended to take about three times as long as planned. There were also a few organized discussions. The workshop was longer than usual in the hope that people would have time to do some serious computation or software development.

List of Participants and Talks or Demos

Gilbert Baumslag A new interface for group theory
David Bayer Graphical view of Tietze transformations
Jim Cannon Partition rules for hyperbolic groups
Greg Conner Coset enumeration
Bill Floyd Computation in Gp{ a,b,c | a^2, b^2, c^2, (ab)^2, (bc)^3, (ca)^7, (abc)^23}
Bob Gilman Formal languages associated to groups
George Havas Computation in abelian groups
Derek Holt Quotpic and the isomorphism problem
Chuck Miller Some new presentations of the trivial group
Leon Moser
Roger Needham The Knuth-Bendix procedure and infinite rewrite systems
Mike Newman Computation in polycyclic groups
Eamonn O'Brien Magma and GAP
David Peifer
Sarah Rees The existence of free quotients
Igor Riven Computer languages for algebraic computation
Mark Sapir The Automate project for semigroups
Martin Schoenert GAP -- A system for computational group theory
Hamish Short A new interface for group theory
Charles Sims Automating the proof of a theorem of Wicks
Stephen Watt The A# language
Peter Webb Experiments related to Alperin's Conjecture

Environment

The administrative and technical staff provided excellent support both while the workshop was being planned and during the workshop itself. The participants seemed to feel very much at home. The layout of the computers worked very well in promoting interaction among the participants. Some people needed more computational power than the Center had available and used remote machines for this purpose. This arrangement was satisfactory, but it was suggested that one or two larger machines such as a SPARC 10/52 with two processors, at least 128 meg of RAM, and 2 gigabytes of disk 2 would be appropriate. (Such a machine would cost about $30,000).

Results

There were a number of instances in which people working on similar problems made contact for the first time. Further, some serious programming and serious experimentation using existing programs occurred. The most significant accomplishment of the workshop may turn out to have been the discussion of what constitutes an appropriate graphical user interface. This topic was the subject of a formal discussion group and of several informal discussions. Most significant group theoretic computation is now done by specialists using command line interfaces. Graphical interfaces offer the possibility that nonspecialists and even nonmathematicians might have useful access to the power of group theoretic packages and programs. This discussion has just begun.