I am a post-doc in the department of mathematics at the University of Iceland, working on the theory of equivariant moving frames, originally developed by my PhD thesis adviser Peter Olver.

My thesis combined Cartan's equivalence method and the equivariant frame for pseudo-groups to define Involutive Moving Frames. I am currently working on the further development of this generalization of the equivariant moving frame, but this theory touches upon many different fields, such as differential geometry, partial differential equations and Pommaret bases (a special type of Gröbner bases).

Papers and preprints:

  • Arnaldsson, Ö., Reduced Cartan characters for polynomial ideals and termination of Cartan's equivalence method, preprint, 2017. pdf
  • Arnaldsson, Ö., Involutive moving frames, preprint, 2017. pdf

Expository Writings:

  • A basic introduction to congruence and equivalence problems
  • A proof that the linearization of an involutive PDE is involutive, based on Pommaret bases
  • An introduction to Pommaret bases, which are Groebner bases with some special properties
  • A paper on reduction of order of Hamiltonian systems

Slides and other writings

Contact Information:

    I can be reached by email at ornarnalds [at] hi.is