Algorithms for acylindrically hyperbolic groups

Lawk will work in the field of Geometric Group Theory. More specifically, he will research relatively hyperbolic groups and the profinite topology. One of the first questions he will study is the following:

Suppose a finitely generated group G is hyperbolic relative to a finite collection of abelian subgroups. Find natural assumptions under which the double cosets of quasiconvex subgroups will be closed in the profinite topology on G.