- Constructive Topology: especially development of the theory of Bishop spaces, a function-theoretic approach to general topology within BISH*, where BISH* is Bishop's informal system of constructive mathematics BISH equipped with inductive definitions with rules of countably many premisses.
- Constructive Analysis.
- Constructive Lipschitz Analysis: study of the role of Lipschitz functions in constructive analysis and of the extension theorems of Lipschitz functions (McShane-Whitney extension theorem, Kirszbraun theorem) within BISH.
- Constructive Combinatorics.
- Constructive Computability Theory at Higher Types.
- Brouwer's Intuitionism.
- Euclidean and Non-Euclidean Geometries.
- Homotopy Type Theory.
- Formalization of mathematics using the proof-assistant Minlog.
Last modified: 30.06.2017