The field of geometric and numerical analysis is witnessing significant developments, with a focus on advancing the understanding of shape spaces, differential systems, and their discretization. Researchers are exploring innovative methods for discretizing Dirac systems and port-Hamiltonian systems, which has led to the development of numerical integrators and constraint algorithms. Furthermore, novel techniques are being introduced to improve the efficiency and accuracy of simulations, such as frequency-domain singularity subtraction for time-domain scattering problems. The study of polyhedral manifolds has also seen substantial progress, with new results on the connectivity of these manifolds through refolding. Additionally, bounds are being established for D-algebraic closure properties, and new methods are being developed for computing lower bounds for the reach of submanifolds. The space of Sobolev curves is another area of active research, with advancements in discrete geodesic calculus and the development of convergent discretization methods. Noteworthy papers include:

• All Polyhedral Manifolds are Connected by a 2-Step Refolding, which provides a groundbreaking result on the connectivity of polyhedral manifolds.
• Discrete Geodesic Calculus in the Space of Sobolev Curves, which presents a comprehensive Riemannian calculus for the space of curves with a Sobolev metric.