Thompson's group F
by Dr Murray Elder
Abstract: In this talk I will discuss the (new) ideas of random subgroups of groups, where the ideas come from and apply to cryptography. The basic idea is this: take a group G and represent its elements somehow (as words in generators, or something else). "Randomly" pick k of these reps and look at the subgroup of G they generate. With what probability would you get - the trivial group, a free group, the whole group, etc? We show that for Thompson's group F some interesting things happen (in contrast to other groups like Braid groups where subgroups are free with probability 1, allegedly). This is work, which involves combinatorics, analysis and (geometric) group theory, is joint with Sean Cleary, Andrew Rechnitzer and Jennifer Taback.
For More Information: Lawrence Reeves email: L.Reeves@ms.unimelb.edu.au