  Geometric aspects play an important role in the construction and analysis of
structure-preserving numerical methods for a wide variety of ordinary and
partial differential equations. Here we review the development and theory of
symplectic integrators for Hamiltonian ordinary and partial differential
equations, of dynamical low-rank approximation of time-dependent large matrices
and tensors, and its use in numerical integrators for Hamiltonian tensor
network approximations in quantum dynamics.
