Since the time of the ancient Greeks, mathematicians have been studying the abstract notion of space. In the last century, it became apparent that a large part of this study can be expressed in the mathematical language of algebra. For applications in physics, interest arose in quantum spaces, which, within this framework, can be described using so-called non-commutative algebras. In my thesis, I study quantum symmetric spaces using the language of non-commutative algebra. I am particularly interested in their symmetries and their connections with special mathematical functions. The most notable results in the thesis concern the connections between Kashiwara’s crystal theory of quantum groups and Macdonald polynomials. It turns out that this crystal theory entails hidden symmetries which, at the level of the Macdonald polynomials, correspond to known symmetries in the deformation parameter. This allows us to view familiar results through a new lens.
Stein Meereboer's academic career:
- 2017–2022 Bachelor’s and Master’s in Mathematics at Utrecht University
- 2022–2026 PhD in Mathematics at Radboud University Nijmegen
- 2026–2028 Postdoctoral researcher at the MPIM in Bonn