New comprehensive review on Topology in Soft and Biological Matter

The review was recently published in Physics Reports

Topology is a branch of mathematics that deals with the properties of figures or objects that remain unchanged under "continuous" deformations—deformations that do not involve "cutting" and "sewing" the object in question. An everyday example is shoelaces, where the process of tying involves passing one end under the other to create a more robust structure: if we were to glue the ends of the lace together, the knot would remain completely locked within the lace itself, and the only way to untie it would be to cut it.

Topology plays an essential role not only in understanding more abstract objects in mathematics (for example, in the very definition of a "knot" in mathematics) but also—more or less spontaneously—finds significant applications in various contexts. These range from theoretical physics (field theories and Feynman path integrals) to the statistical mechanics of soft matter and some of its compounds (polymers, liquid crystals, and other complex fluids), and to molecules of fundamental importance in biology (DNA, RNA, and proteins). Given the vastness and inevitable specialization in the various aforementioned fields, a common language that reveals and integrates their shared traits would be desirable and greatly beneficial for the different communities.

The review titled "Topology in Soft and Biological Matter," recently published in Physics Reports, aims precisely at this goal: starting from the rigorous language of knot theory and field theories in physics, to the latest computational techniques and algorithms for quantifying the topological properties of real molecules, the work presents an overview of the state of the art of the applications of topological concepts in mathematics, physics, chemistry, and biology.

The review, coordinated internationally by Prof. Luca Tubiana of University of Trento (a former student of the School), concludes a four-year journey of the COST Action CA17139 EUTOPIA: the initiative, funded by the European COST program, saw the participation of scientists from almost all European Union countries and some of its partners (such as Turkey, Israel, and the USA). The review, also coordinated by Prof. Tubiana, was realized thanks to the intense collaborative effort of 59 scientists from as many institutions from the European Union countries and several of its partners.

The contribution of SISSA to the initiative and the review was central. Prof. Angelo Rosa served as the coordinator of the EUTOPIA working group "Polymeric and Fibrous Topological Materials", organizing and supervising the final drafting of the more specific sections of the review on polymers and viscoelasticity. Additionally, Prof. Cristian Micheletti contributed to the section of the review on knots in polymers and biopolymers.