[1] He subsequently pursued doctoral studies in Mathematics at the University of Warwick under the supervision of David Epstein where he received a PhD in 1988.
[8] Early notable results of Bowditch include clarifying the classic notion of geometric finiteness for higher-dimensional Kleinian groups in constant and variable negative curvature.
He showed, however, that in dimensions n ≥ 4 the condition of having a finitely-sided Dirichlet domain is no longer equivalent to the standard notions of geometric finiteness.
In a subsequent paper[10] Bowditch considered a similar problem for discrete groups of isometries of Hadamard manifold of pinched (but not necessarily constant) negative curvature and of arbitrary dimension n ≥ 2.
[14] Bowditch's work relied on extracting various discrete tree-like structures from the action of a word-hyperbolic group on its boundary.
[16] One of the consequences of Bowditch's work is that for one-ended word-hyperbolic groups (with a few exceptions) having a nontrivial essential splitting over a virtually cyclic subgroup is a quasi-isometry invariant.
In a 1999 paper[20] Howard Masur and Yair Minsky proved that for a finite type orientable surface S the curve complex C(S) is Gromov-hyperbolic.
This result was a key component in the subsequent proof of Thurston's Ending lamination conjecture, a solution which was based on the combined work of Yair Minsky, Howard Masur, Jeffrey Brock, and Richard Canary.