T1: Topological Soft Matter

Topology is today emerging as a strong and unifying concept in the development and design of new materials, prominently in soft matter. For example, topological defects in active and passive complex fluids are central for the material’s equilibrium and out-of-equilibrium properties, entanglement and knotting of soft physical objects or material fields enable creation of novel soft topological materials, and topological concepts allow for design and realization of field-based quasiparticles, such as torons, hopfions and skyrmions. Of particular focus will be the role and characterization of singular topological defects and solitons, including when knotted. Overall, the goal of this short course is to train participants in current state-of-the-art concepts in topological soft matter.

Topics covered:

• Basic topological concepts and invariants used and explored in different passive and active topological soft-matter systems.•

• Experimental techniques for studying topological soft matter.

• Theory, modelling and AI methodological approaches for studying topological soft matter.

• Connections with non-soft-matter topological materials, such as with chiral magnets.