Johnson Allan Kessy

Master of science Johnson Allen Kessy will Wednesday April 12, 2023, at 10:15 hold his disputas for the PhD degree in Science. The title of his thesis is: 

"Cartan-Geometric Approaches to Submaximally Symmetric Ordinary Differential Equations"

Summary:

This thesis is concerned with a symmetry classification problem for ordinary differential equations (ODEs) that dates back to Sophus Lie. We focus on higher order ODEs, i.e. scalar ODEs of order greater than or equal to 4 or vector ODEs of order greater than or equal to 3, up to contact transformations. The maximal contact symmetry algebra dimensions for these ODEs are known. We determine for all higher order ODEs the submaximal (i.e. next largest realizable) contact symmetry dimensions. Using the known contact fundamental (generalized Wilczynski or C-class) invariants for higher order ODEs, we also determine submaximal symmetry dimensions for several classes of the ODEs that are contact invariant. Moreover, we give a complete local classification of all submaximally symmetric vector ODEs of C-class, i.e. ODEs with symmetry dimensions realizing submaximal symmetry dimensions that are characterized by the vanishing of all generalized Wilczynski invariants. Our results refine the classical results for scalar ODEs, and also provide generalizations of those results to vector ODEs.

Evaluation Committee

• Professor Joël Merker, University of Paris-Saclay, Orsay Cedex, France (1. Opponent)
• Professor Irina Markina, University of Bergen (2. Opponent)
• Professor Hilja Huru, IMS, UiT (intern member and leader of the committee)

Supervisors 

• Associate Professor Dennis The, IMS, UiT (main supervisor)
• Professor Boris Kruglikov, IMS, UiT (co-supervisor)

The Disputas will be led by Professor Martin Rypdal, head of the Department of Mathematics and Statistics.

Streaming site

The disputas and trial lecture will be streamed from these sites:

Disputas (10:15 - 15:00)

Trial Lecture (9:00 - 9:45)

Thesis

The thesis is available through Munin.