Trial Lecture and Thesis Defense - Wijnand Sebastian Steeneker

Master of Science Wijnand Sebastian Steeneker will hold the Trial Lecture and Thesis Defense for the PhD degree in Science on Tuesday, September 22, 2026.

Trial Lecture

The Trial Lecture will take place 10:15 - 11:15.

The title of the Trial Lecture is:

« Integrability and nonintegrability in finite and infinite dimensional systems »

Thesis Defense

The Thesis Defense will take place 12:15 - 15:00.

The title of the thesis is:

« Invariants, Integrals and Geometric Variational Problems »

Abstract

This thesis concerns the study of invariants and integrals of differential equations through the geometric theory of jet bundles. The work is organized around two common threads.

The first is regarding the integrability and variationality of dynamical systems. We establish that for a generic spacetime in the Koutras-McIntosh family there are no Killing tensors up to degree 6. We then turn to the variationality of conformal geodesics: we show that the parametrized conformal geodesics in dimension 3 are not variational, whereas the unparametrized conformal geodesic equations in dimension 3 are variational. In the theory of invariant variational calculus, we develop methods for computing singular extremals, and show that these are effective in practice as well. We show that jets of initial data for classes of BKM PDEs, recently introduced by Bolsinov-Konyaev-Matveev, can be approximated up to arbitrary order by finite-gap solutions. In particular, we obtain jet-density for the classes containing the Korteweg-de Vries and Camassa-Holm equations, respectively.

The second common thread concerns differential invariants of Lie group and Lie pseudogroup actions. Continuing in the invariant variational calculus, we construct explicit invariant contact forms of order zero from the symbols of scalar differential invariants. We also explain how to compute the invariant Euler-Lagrange equations for rational differential invariants (without needing to appeal to moving frame methods). For Carrollian spacetimes, we compute the differential invariants from the geometry of the screen bundle. We count the number of invariants, and compute the intrinsic torsion and intrinsic curvatures through Spencer cohomology and describe an explicit representative of the intrinsic curvature.

Supervisory Committee

• Professor Boris Kruglikov, Department for Mathematics and Statistics, UiT (Main Supervisor)
• Professor Denis The, Department for Mathematics and Statistics, UiT

• Associate professor Eivind Schneider, Department for Mathematics and Statistics, UiT
  
  

Evaluation Committee

• 1st Opponent: Dr. Alexey Bolsinov, Reader in Mathematics, Department of Mathematical Sciences, Loughborough University, United Kingdom
• 2nd Opponent: Dr. Arman Taghavi-Chabert, Assistant Professor, Department of Geometry, Faculty of Mathematics and Computer Science, University of Lodz, Poland.
• Internal member and leader of the committee: Professor Hilja Lisa Huru, Department for Mathematics and Statistics, UiT, Norway.

Streaming

The Trial Lecture and Thesis Defense will be streamed via Panopto:

Trial Lecture (10:15 - 11:15)
Watch the Trial Lecture

Thesis Defense (12:15 - 15:00)
Watch the Thesis Defense

Thesis

The thesis is available in Munin:

View the thesis in Munin