Currently I’m interested in Programming Language Theory and in the use of programming in the foundations of Mathematics and Physics.

I have a special interest in problems related to the Axiomatization Problem of Physics, which can be viewed as a “stable” version of the classical Hilbert’s sixth problem.

• Parameterized Enriched Topoi:
  • the aim of this project is to generalize the theory of Grothendieck topoi to a context in which:
    • the sheaves are enriched;
    • the enrichment is not only over a fixed monoidal category, but actually over a parameterized family of them.
• Geometric Cohomology:
  • for Grothendieck topoi the intrinsic geometry is described by Cohesive Geometry, which provides the description of geometric structures as entities related to the intrinsic Differential Cohomology. in this project we plan to extend cohesion to the parameterized enriched context in such a way that Differential Cohomology is replaced with a general Geometric Cohomology, whose cocycles:
    • take values not on $\infty$ -groupoids, but rather take on families of algebraic entities defined on the parameterized family of monoidal categories;
    • classify geometric entities other than connections on higher bundles.

For a precise description of the projects, with a step-by-step prescription of how to follow them, see here. For a talk about them, see here.