Johannes Oude Groeniger

Research interests

• Mathematical relativity;
• geometric PDE's;
• Hamiltonian dynamics.

Current research

My research, under supervision of Hans Ringström, was in the interplay of dynamics and geometry, concerning Einstein's equations in the setting of cosmology. Many interesting geometric and dynamical questions and problems arise naturally in this theory, concerning e.g. the influence of symmetry, long-term stability of solutions or the formation of singularities. For example, I have studied the nature of the initial singularity in so-called Bianchi \(\rm{VI}_0\) spacetimes. These spacetimes contain a high degree of symmetry (homogeneity), and the precise symmetry has a large influence on the dynamics. My other research projects concern the so-called exceptional Bianchi spacetimes, in the presence of stiff fluid matter, as well as more general formation of big bang singularities in regimes of large mean curvature and in the presence of scalar field matter. Lastly, as an aside, I have an interest in the dynamics of resonant oscillators in Hamiltonian dynamics. 

I defended my PhD in late 2023 but I am currently not actively involved in research.