Arithmetic nature and continuity of growth rates of Coxeter systems

First, I will talk about the space of Coxeter systems and show that the growth rate is a continuous function on the space. This result on the continuity of the growth rates is a geometric group theoretic extension of the results on the growth of hyperbolic Coxeter groups of dimension 2 and 3 proved by Floyd and Kolpakov. Second, I will explain an application of the result on the continuity to the study of arithmetic nature of growth rates of Coxeter systems. The second part of this talk is based on joint work with Naomi Bredon.