My name is Jagna Wiśniewska and I am a Postdoctoral researcher with prof. Will Merry. In 2017 I have obtained a Ph.D. degree at the VU University, Amsterdam under the supervision of prof. Federica Pasquotto. My field of research is symplectic geometry. 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. My recent result was extending the notion of Rabinowitz Floer Homology to non-compact hypersurfaces.
Chocolate, satellites and the beauty of math - explaining Morse theory by observing chocolate flow on doughnuts and connecting it to the movements of satellites using Floer theory.