Over the last century, logical and computational phenomena, in addition to more traditional physical ones, have provided mathematics with significant inspirations and been studied intensively. Today, as a consequence, mathematical logic and theoretical computer science have become mature as academic disciplines. From my (or a mathematician's) point of view, however, the very concepts of logic and computation have not yet been captured in a completely satisfactory manner especially because they have been studied mostly by syntactic and/or synthetic methods. My research is primarily concerned with this fundamental problem, and I aim to establish a mathematical, in particular semantic and analytic, foundation of logic and computation, whence of (constructive) mathematics as well.
I am also interested in category theory, more broadly algebra, and its interplay with logic and computation, known as categorical logic.
In addition, the recent advent of homotopy type theory has brought a novel, topological viewpoint into these fields. I am especially interested in such an interaction between logic, computation, category theory and topology.