Research Projects
Feel free to get in touch if you're interested in doing a research project on any of the topics listed below.
Current Topics
- Quantum Integrable Systems
...where we study N-body problems in Quantum Mechanics, focusing specifically on Calogero-Ruijsenaars type models, that permit exact analytical solutions through an abundance of conserved quantities.
- Lie Groups, Lie Algebras, and Representation Theory
...where we explore continuous symmetries and their linear realizations by examining how geometric properties translate into infinitesimal algebraic structures and studying classification theorems that bridge abstract algebra with applications in geometry and physics.
- Spin Chains and Quantum Groups
...where we consider Heisenberg's model (1928) for ferromagnetism and its solution by Bethe (1931) that started the field of quantum integrable systems and culminated in the discovery of quantum groups (Faddeev et al. 1980s).
- Solitons and the Inverse Scattering Transform
...where we study and apply a nonlinear version of the Fourier transform to solve partial differential equations with particle-like solutions (solitons).
- Gauge Theory and Topological Quantum Field Theory
...where we build field-theoretic models (e.g. Chern-Simons theory) where local symmetries yield metric-independent invariants thereby bridging abstract differential geometry with modern theoretical physics and highlighting applications in low-dimensional topology and topological quantum computing.
- Gravity in Non-Euclidean Spaces
...where we figure out what Newtonian gravity looks like in higher-dimensional non-Euclidean spaces and discover the hidden symmetry groups underlying the curved Kepler problem. As a bonus, we derive Kepler's laws of planetary motion in curved spaces.
Past Projects
Here's a selection of past projects:
- 2026, Tim Folgering, Chern-Simons theory and its relation to inflation
- 2025, María Díaz Marrero, Spin Chains and their Symmetries using the Bethe Ansatz
- 2024, Jasper Hamhuis, Harmonic Oscillators in Spaces of Constant Curvature
- 2024, Tunay Oruç, Integrable Open Quantum Systems
- 2023, Destin Nobach, Hidden Symmetries of the Kepler Problem in n Dimensions