Topological recursion and classification of multi-stranded biopolymer configurations
Seminar Room 1, Newton Institute
In this talk I will present the formalism of so-called "topological recursion" and demonstrate how it can be applied to provide a complete classification of multi-stranded configurations of biomolecules. The "topological recursion" is a beautiful and rather sophisticated method arising from random matrix theory, which already found many applications and is currently under very active study in random matrix / statistical physics / high energy physics communities. In particular, I will present how to use this formalism to classify and compute all topologically inequivalent configurations of biomolecules, consisting of arbitrary number of strands, connected by arbitrary number of bonds or basepairs. This solution provides a new application of random matrix theory in the context of biophysics. Our solution has also an independent interpretation in pure mathematics, i.e. it provides certain important characteristics of moduli spaces of Riemann surfaces with boundaries.