Since 1/10/2019 I'm affiliated to the departement of Mathematics (research group Fundamental Mathematics) as PhD student. My research, which is entitled 'Symplectic operators and their representation theory', is under the supervision of Prof. Sonja Hohloch (dynamics part) and Prof. David Eelbode (operator theory part) and will mostly concern symplectic techniques in analysis supported by methods from algebra. The latter includes representation theory and Lie theory in order to reveal the underlying symmetries of operators (such as the Dirac operator) and dynamical systems (in particular Hamiltonian systems, e.g. vortex dynamics) and to study their internal interaction.