The winner of the NR prize this year is Michael Gjertsen with his thesis Metaplectic Transformations for Gabor Frames and Equivalence Bimodules. His thesis advisor was Franz Luef.

The master thesis of Michael Gjertsen discusses the structure of multi-variate regular Gabor frames and of Heisenberg modules over noncommutative tori by using tools from symplectic geometry and the theory of metaplectic representations. Gabor analysis is a subject in time-frequency analysis with close ties to both information and communication technology, as well as theoretical and applied physics.

The thesis spans more than 250 pages and is founded on an impressive variety of advanced mathematical tools, encompassing diverse fields such as symplectic geometry, operator algebras and Gabor analysis. Many of the results in the thesis were developed from first principles, and Gjertsen has derived several important theorems with proofs on his own. Of the different results contained in the thesis, those related to regular Gabor frames are going to have a lasting impact. These are, in fact, the first general results concerning the structure of multi-variate Gabor frames and give potential for extending known results for univariate Gabor frames to the multi- variate case, for example Daubechies’ density theorem. The thesis of Gjertsen is unusually extensive and his work builds upon a large variety of advanced theory within diverse mathematical areas for which there are no regular courses taught at NTNU.

Gjertsen did a BSc in Physics, and the continued into the 2-year MSc programme in Mathematics at the Department of Mathematical Sciences, NTNU. As a part of his master studies, he took 10 courses and got A in every single one of them.

Gjertsen is a worthy winner of the NR prize for 2022.