Do You know any successful applications of the geometric group theory in the number theory? GTG is my main field of interest and I would love to use it to prove new facts in the number theory.



Links between Geometric Group Theory and Number Theory
Another reference showing the connections between geometric group theory and number theory is the book of 
A. Lubotzky on "Discrete Groups, Expanding Graphs and Invariant Measures."


There are many special topics where a connection between number theory and geometric group theory arises. As an example see <http://arxiv.org/abs/0901.1458>.


