Abstract: Symplectic capacities are important objects in the field of symplectic topology. In particular, they constitute a tool to check if a symplectic manifold can be embedded into another one. Unfortunatelly, they are notoriously hard to compute.
The Hofer-Zehnder capacity is the supremum over the set of all "admissible" Hamiltonians. In this talk, I will present my attempt to derive a lower bound for the Hofer-Zehnder capacity of the disk bundle over the lens space  $L(p;1,\cdots ,1)$ by the construction of a specific admissible Hamiltonian. The corresponding dynamics on the lens space will lead to magnetic geodesics which are solutions to the geodesic equation modified by a Lorenz force term.