The mathematical concept of topology is now widely applied in condensed matter systems providing a fresh perspective for the understanding and prediction of many physical phenomena. The Action focuses on techniques for the creation and annihilation of topological textures and on their static and dynamic properties that form a vibrant field of research.

A variety of topological textures are observed and are ubiquitous in the sciences (physics, materials, biology, chemistry). Examples are domain walls, vortices, skyrmions, and hopfions in bulk materials, with a big challenge now posed by the complexity added by the third dimension. Their dynamics and response to external probes are often counter-intuitive and they are linked to topology in surprising ways. These properties make them promising for applications in sensors, logic and non-Boolean devices, logic-in- memory computing, and neuromorphic or quantum computing applications. Related physical
systems include magnets, ferroelectrics, optics and topological light, ultra-cold atoms and superfluids, superconductors, liquid crystal and similar systems, quantum systems with a topological band structure, and others.

The area of condensed matter benefits greatly from the interaction between experiments, theory, and computations on topological textures. Improved techniques allow for observations at the nanoscopic and picosecond scales. However, progress is driven by small and fragmented communities of physical scientists and by a separate community of applied mathematicians. This network will bring together in a wider network the separate sub-communities working on the various physical systems, it will combine expertise and boost synergies. It aims to develop a unified framework for topological condensed matter systems.