The two-boost problem and Lagrangian Rabinowitz Floer homology, with Kai Cieliebak, Urs Frauenfelder and Eva Miranda, arXiv preprint arXiv:2412.08415. (2024)
b-Contact structures on tentacular hyperboloids, with Michael Vogel in Journal of Geometry and Physics, Vol. 191, pp. 104867. (2023)
Computing the Rabinowitz Floer homology of tentacular hyperboloids, with Alexander Fauck and Will J. Merry in Journal of Modern Dynamics, vol. 17, pp. 353-399. (2021)
Rabinowitz Floer homology for tentacular Hamiltonians, with Federica Pasquotto and Rob Vandervorst in International Mathematics Research Notices, vol. 2022, no. 03, pp. 209-265. (2020)
Bounds for tentacular Hamiltonians, with Federica Pasquotto in Journal of Topology and Analysis, Vol. 12, No. 01, pp. 209-265. (2020)
In 2024 I was invited to give two online talks at the Gamma Seminar at the Faculty of Physics, University of Warsaw. These two talks give a comprehensive introduction to my area of research. You can find their recordings below:
In this talk I give an introduction to my field of research. I start with presenting the definition of Morse homology, which relates the dynamics given by the gradient flow of a function to the singular homology of the underlying manifold. Further on, I show how the Morse homology inspired Floer to construct his own algebraic invariant, which relates the 1-periodic orbits of the Hamiltonian flow to the topology of the underlying symplectic manifold.
Building on my previous talk, I show how the Floer homology can be used to analyze the dynamics of autonomous Hamiltonian systems. In this talk, I present my own research, which focuses on the question of existence of periodic orbits of Hamiltonian flow on non-compact energy hypersurfaces.