School Seminars and Colloquia

Random subgroups of Thompson's group I

Statistical Mechanics/Combinatorics Seminar

by Murray Elder

Institution: Dept. Mathematics, Stevens Institute of Technology, USA
Date: Thu 19th July 2007
Time: 11:00 AM
Location: Russell Love Theatre, Dept. of Mathematics and Statistics, The University of Melbourne

Abstract: In this talk I will introduce Thompson's group from scratch - if you
don't know the definition of a group it should still make sense - Thompson's
group a beautiful combinatorial object that's fun to work with. I can be
viewed as a set of certain ("reduced") pairs of rooted binary trees. I will
run through how the group multiplication works, how to see the multitude of
subgroups it has using trees, and discuss some approaches to counting its
elements. The theorem will be this: The generating function for the number
of "reduced" binary tree pairs is D-finite but not algebraic, and is related
to the generating function for the squares of Catalan numbers.

Joint work with Sean Cleary, Andrew Rechnitzer and Jennifer Taback.

For More Information: Dr. Iwan Jensen Phone: +61 3 8344 5214