Department of Electronics and Information Systems

Master Thesis Proposals

The master thesis topics we propose can be situated in the field of harmonic analysis. We like to use algebraic or analytic methods, or a combination thereof. Connections with representation theory or with the algebraic structures (such as e.g. Lie (super)algebras or quadratic algebras) describing the symmetries of quantum integrable systems often give additional interpretations to and insights in the mathematics we investigate. 
From a technical point of view, we use a variety of methods: Clifford algebras, Lie (super)algebras, quadratic algebras, orthogonal polynomials and special functions, fractional calculus, combinatorics, …
Not all these methods are present in every thesis subject of course.

We always tailor topics to fit the specific interest of students, within the areas described above. Depending on the specific topic, we may even look at ongoing research and try to contribute to it. 
Below you may find a number of (older) topics to give you an idea of what is possible. Please contact Hendrik De Bie for more information.

In case you are specifically interested in Lie superalgebras, supermanifolds, or applying category theory in representation theory, you can also contact directly our team member Sigiswald Barbier.

Our research group is a part of the Faculty of Engineering and Architecture. As such we are also happy to act as an intermediary for students interested in engineering problems with a deep mathematical flavor. For example, if you are interested in computational electromagnetics and the numerical analysis behind it, we can propose to collaborate with Kristof Cools (see users.ugent.be/~krcools/).  You can also have a look at the research interests of other members of Foundations Lab, in the field of probability, or quantum engineering, see (https://www.ugent.be/ea/elis/en/research/foundationslab)

Some examples of previous master (or bachelor) dissertations:

  • Generalized q-Bannai-Ito, Askey-Wilson and q-Onsager algebras
  • The higher rank Dirac-Dunkl model and the Bannai-Ito algebra
  • Tensor Representations of the Orthosymplectic Lie Superalgebra
  • The quantum mechanical Segal-Bargmann transform using Jordan algebras
  • The Clifford-Helmholtz system and related Fourier transforms
  • Discrete analytic functions
  • The Radon transform
  • Descriptions of conformal transformations using geometric algebra