My research interests lie in the areas of discrete geometric mechanics and discrete differential mathematical modeling. In particular, I seek to develop and study discrete models of infinite dimensional systems which preserve underlying geometric structures. Discrete models of this type usually lead to novel numerical methods, so called structure-preserving integrators, which capture the dynamics of the system without energy or momenta loss and preserve momentum maps in the discrete realm. In my PhD thesis I developed the first variational integrator for Euler fluids. Since then, our methods have been developed further and are now applicable to a great variety of infinite-dimensional systems, such as magnetohydrodynamics or complex fluids. My current research is centered on a link between noncommutative geometry and discretization. Our goals include, in particular, creating a new model of discrete differential geometry that leads to a structure preserving discretization of general relativity.