Research interests
- Integrable Hamiltonian systems and their bifurcation behavior, in particular (hyper)semitoric systems and their (non)degenerate singularities, and interactions with Hamiltonian S^1-actions.
- Symplectic geometry, Floer theory and its applications to symplectic and contact dynamics (homoclinic points, growth behaviour)
- Cauchy-Riemann-Fueter PDE and its bubbling-off analysis, associated Hamiltonian PDEs on Hilbert spaces, hyperkähler Floer theory, relations to Clifford analysis.
- Optimal transport and its application to integer partitions and integrable systems.
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Morse theory and its application to integrable systems and n-categories.
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Symplectic numerics.