Research
Research Interests: contact and symplectic geometry, pseudoholomorphic curves and Hamiltonian dynamics.
Publications
(with Marcelo Alves, Umberto Hryniewicz, Mathias Meiwes and Pedro Salamao) The Denvir-Mackay theorem for Reeb flows (work in progress, but details are also partially written up in my thesis).
(With Barney Bramham) Spectral invariants for non-compactly supported Hamiltonians on the disc, and an application to the mean action spectrum arXiv:2403.07863
(With David Bechara Senior and Patrice Le Calvez) The asymptotic mean action and the asymptotic linking number for pseudo-rotations, arXiv:2312.17087
(With Marcelo Alves, Lucas Dahinden and Mathias Meiwes) C^0-stability of topological entropy for Reeb flows in dimension 3, arXiv:2311.12001
(with Rohil Prasad) Generic equidistribution for area-preserving diffeomorphisms of compact surfaces with boundary, arXiv: 2211.07548
Applications of contact homologies to the dynamics of low dimensional Hamiltonian systems, Ph.D. dissertation, Ruhr-Universität Bochum
Hutchings' inequality for the Calabi invariant revisited with an application to pseudo-rotations. arXiv:2102.09533.
(with Marcelo Alves). “Reeb orbits that force topological entropy”. arXiv:2004.08106.
(with Farrukh Mukhamedov and Uygun Jamilov). “On Nonergodic Uniform Lotka–Volterra Operators”. Mathematical Notes 105, pp. 258–264.
(with Rasul Ganikhodzhaev, Farrukh Mukhamedov, and Izzat Qaralleh). “Genetic Volterra algebras and their derivations”. Communications in Algebra 46, pp. 1353–1366.
(with Rasul Ganikhodzhaev). “Quadratic homeomorphisms of the two-dimensional simplex and their trajectories”. Topics in Functional Analysis and Algebra, Contemporary Mathematics 672, pp. 179–184.