Generic subsets of Thompson's group

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.