Research interests

I work at the intersection of computability theory and of group theory.

My main contribution is to show that tools from computable analysis are relevant to study certain decision problems in group theory, in particular for decision problems about groups that are described by means other than finite presentations.  

However, because many pathological phenomena occur in computability in group theory, that do not naturally occur in computable analysis, this also requires the exploration of objects previously not considered in computable analysis. 

The main example of the above is the study of the space of marked groups: the space of marked groups is a Polish space, but it is not computably Polish because it is not computably separable. Because most of the spaces previously studied in computable analysis are computably separable, the computable topology coming from a computable metric had never been defined without an implicit assumption of computable separability.

I am also interested in classifying group-theoretic decision problems using Weihrauch reducibility.