Generic subsets of Thompson's group
- Date: 11/21/2006
Murray Elder (Stevens Institute of Technology)
University of British Columbia
Richard Thompson constructed an example of a group which is called
'F'that has many unusual properties. One way to consider its elements
is in terms of pairs of rooted binary trees. This viewpoint lends
itself nicely to counting subsets of elements with particular
properties. Meanwhile in cryptography, interest turned to finding
algebraic structures (like groups) on which to base cryptosystems.
These groups should have problems or properties that are hard to decide
(in some sense). A property of a group or set is 'generic' if one can
place a probabilistic measure on elements so that the subset of
elements enjoying the property has measure 1. So in an effort to make
sense of this we try it out on Thompson's group F - we define a measure
and look for properties of the group, or subgroups of the group, that
are in this sense 'generic'.
This is joint work with Jennifer Taback, Bowdoin, Maine, and should be accessible to all.
Discrete Math Seminar 2006
