PIMS Special Speaker-Problems in computational topology: Where pure mathematics meets computer science

Some of the core problems in low-dimensional topology involve algorithms to identify and compare topological spaces. However, where these algorithms exist, they are often infeasibly slow and difficult to implement.
Here we outline the ways in which topological results can be blended with traditional computer science techniques to improve these algorithms. In particular, we examine (i) the enumeration of normal surfaces, a key component of several recognition algorithms, and (ii) building a census of triangulations, a requirement for identifying minimal representations of a topological space.