Mathematical modeling of physical systems.
Broadly speaking, I am interested in the mathematical modeling of
physical systems using the methods of modern (algebraic or
differential) geometry. In particular, I have experience working
in the following areas:
- Stability and control theory for hybrid systems;
- Methods of noncommutative geometry in the theory of completely integrable Hamiltonian systems;
- The geometric approach to integrable hierarchies of PDEs (e.g. the KdV and KP equations) via infinite-dimensional Grassmannians.
Formal methods in computer science. I also have
a life-long interest in computer programming and its foundations,
including type theory and formal logic.
- I have some experience in computer-assisted theorem proving using higher order constructive logics (e.g. the Coq proof assistant) and certified (a.k.a. correct-by-construction) programming.
- In particular, I was a member of the EU-funded CARVE project, in which I developed a certified interpreter for Behavior Trees which has been deployed on actual hardware (the R1 robot) at the Istituto Italiano di Tecnologia.