Modern symplectic geometry started as a mathematical
formulation of classical mechanics. It can be used to analyse dynamical
systems arising in classical mechanics, for example trajectories of
charged particles in magnetic fields or orbits of satellites under the
gravitational forces of planets and stars. In my research I have
investigated the existence of periodic orbits for Hamiltonian systems on
a fixed, non-compact energy level. Nontrivial examples of these systems
are too complex to describe their evolution with a precise formula.
Therefore in the analysis of Hamiltonian dynamics in order to
characterise the properties of the system one has to use tools from
different fields of mathematics such as differential geometry (contact
and symplectic geometry), functional analysis (calculus of variations)
and algebraic topology (Floer homology). These tools enable us to
analyse the dynamical behaviour of the systems in question and whether
their properties are preserved under small perturbations.

Before the seminar, at 2:00 pm there will be tea and cookies.