The research interests of the mathematical logic team (Genoa logic group http://logic.dima.unige.it/) range over several fields of the discipline. The main ones include:

• Categorical logic and category theory with applications to constructive mathematics. This includes the study of fibered categories and their properties to describe deductive systems.
• Type theory and its categorical semantics.
• Non-classical logics, modal logics, and geometric logic, and the development of their proof theory.
• Computable mathematics.
• Descriptive set theory, in particular the study of complexity hierarchies coming from logic, algebra, and geometry.
• Classification problems in real analysis and in continuum theory.

The Genoa logic group has ongoing collaborations with various research groups across Europe, like those based in Lausanne, Nice, Aix-Marseille, Helsinki, Stockholm. It has promoted and is part of the informal logic network including the logic groups of the universities of Lausanne, Turin, and Udine (https://logicgroup.altervista.org/?lng=eng), which in particular runs the weekly Cross-Alps logic seminar.

Members of the group are also involved in the following activities and projects:

• «Modalities in Substructural Logics: Theory, Methods and Applications» (https://cordis.europa.eu/project/id/101007627), focused on the systematic study of substructural modal logics and their applications to knowledge representation; legal reasoning; data privacy and security; logical analysis of natural language.
• «Infinity and Intensionality: Towards A New Synthesis» (https://www.oysteinlinnebo.org/inf-int), aiming to the development of a new approach to mathematics, supplementing infinite sets with intensional notions.
• ItaCa (https://progetto-itaca.github.io/), the Italian network of category theorists, with collaborations involving several mathematics and computer science departments.
• The organisation of dissemination events, like the Festival della Scienza di Genova and the Mathematical Olympiad.