Mai Gehrke received a grant from the Free Competition of The Netherlands Organisation for Scientific Research (NWO) intended for the hiring of two Ph.D. students on an interdisciplinary project with Bart Jacobs from ICIS. The two students employed on the project are Sam van Gool and Jorik Mandemaker.
The project, entitledMathematically and Computationally Relevant Dualities, focuses on dualities which are ‘dually’ relevant, both in mathematics and informatics. Within mathematics, dualities underlie fundamental connections between algebra and geometry, and between logical syntax and semantics, e.g. in the various dualities extending Gelfand and Stone. Such dualities also appear in informatics where they relate (program) logics and computations. The aim of this project is to significantly advance interdisciplinary interaction between topological methods in algebra and coalgebraic methods in informatics by engaging two Ph.D. students and two senior researchers in addressing cutting-edge problems pertinent to both disciplines, and to seek shared solutions and shared understanding. Of particular importance in this setting is to unify dualities for enriched discrete and continuous spaces. For mathematics, this project aims to unify topological methods in logic and in geometry and algebra. In computer science terms, this goal may be stated as aiming for a generalization of Abramsky’s ‘Domains in Logical Form’ encompasing probabilistic computing systems.