The past decade has seen striking experimental and theoretical advancements in the fields of biophysics and material science. On the biophysics front, the development of chromosome conformation capture techniques, such as HiC and super-resolution imaging, now permits researchers to probe the organization of chromosomes in unprecedented detail, while single-molecule manipulation techniques and computer aided theoretical studies have conspicuously increased our understanding of DNA and proteins. In material science, optical traps, colloid manipulation techniques and single-molecule experiments are opening up the possibility of creating self-assembling materials, often inspired by Nature, at scales ranging from those of single proteins (i.e. nanometres) up to microns. DNA origami, colloidal suspensions and novel liquid crystals (LC) nano- and micro-structures with complex topologies and unique mechanical and optical properties have been theorized and experimentally realized. Each of these breakthroughs has triggered immense interest for their possible technological applications. The emergence of DNA sequencing techniques holds the promise for the development of personalized nano-medical treatments that could cure millions. The first examples of computer-aided protein design paves the way to applications ranging from the development and use of novel enzymes, to scaffolds for smart materials and nano-reactors. DNA origami and patchy colloids are making possible the creation of complex nano- and micro-scale self-assembling architectures which could be used as super-strong materials, or even micro-factories in which chemistry takes place. Topologically complex liquid crystals are among the most promising materials for advanced soft photonics applications. These advances have also highlighted the role of topology in bio- and soft materials and the importance of modelling and controlling it to improve our understanding and to realize the aforementioned applications. The wealth of experimental data calls for new theoretical ways to characterize entanglements and other topological aspects; at the same time progress in this direction will allow the control and tuning of topological structures in complex systems, permitting the scale up of self- assembling materials to sizes relevant for technological applications and to make their production more reliable.

The impact of research on topological properties of (bio)materials is therefore at a turning point. Until now, much of the theoretical and computational work has laid down the fundamentals for what will happen in the next years, when real-life applications will take advantage of the existing knowledge and discoveries. Therefore, creating a collaborative platform is a crucial step to establish a systematic approach to investigate topological soft materials, which will lead the researchers of the EUTOPIA Network to unravel some of the hottest questions both in soft matter and biophysics, with potentially momentous technological and societal impact.