I'm an associate professor of mathematics in the Information and Communication Technology group in the Department of Computer Science, Electrical Engineering and Mathematical Sciences of the Western Norway University of Applied Sciences.
My main interests are:
- Machine Learning, Deep Learning and Bayesian Statistics
- Functional programming, certified programming and type theory (Haskell, Coq)
- Scientific Computing, Geometric Integration
The main themes of my research so far has revolved around the integration of differential equations (ODEs or PDEs) on manifolds.
There are four themes on which I have particularly focused on:
- Structure preservation How to preserve the differential invariant (volume, symplectic), first integrals (energy), fixed points, periodic orbits, of constrained systems?
- Symmetries Manifolds are often endowed with a natural symmetry: how can integrators respect that symmetry? A particularly important case is that of affine symmetries, related to scaling invariance and the anisotropy problem.
- Constraint reduction A combination of differential equations and algebraic equations leads to a reduction algorithm to obtain a differential equation on a manifold: does the reduction halt? how does the integrator preserve the underlying manifold?
- Software development Development, packaging and distribution of scientific computing software.