dr hab. Franco Ferrari (IF Uniwersytet Szczeciński)

The physics of polymer knots and links: Some analytic and numerical aspects

The physics of polymer knots and links is a multidisciplinary subject. On one side, it is a playground for field theoretical techniques, like the renormalization group method and, more recently, for topological field theories. On the other side, the investigations of the statistical mechanics of polymer rings have also a feedback in field theories. Examples are a few progresses in treating field theories with constraints and a class of identities that allow to simplify complicated interactions in scalar field theories. Moreover, models of polymer knots and links have a range of applications that go beyond the physics of polymers and become relevant to other disciplines, in which the topological properties of quasi one-dimensional objects play an important role. This is the case of magnetohydrodynamics and of some systems of quasiparticles with non-trivial statistics in solid state physics. Nowadays, the behavior of single polymer knots can be checked experimentally and it is possible to create polymer melts containing a very high percentage of polymer rings entangled together. Properties which are too difficult to be studied directly via experiments may be investigated thanks to reliable numerical simulations. In this introductory talk some of the recent experimental, analytical and numerical results in the physics of polymer knots and links will be presented.