Interplay of Topology and Geometry in Polymeric Critical Phenomena

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This project aims to develop new understanding of key topologically driven behaviour in complex polymers such as DNA. The mathematical modelling of the rich geometric behaviour of long-chain polymers and how they change their shape in response to the environment has provided a framework for our understanding of these ubiquitous molecules. Complex polymers such as ring polymers and DNA display topological properties such as knotting and linking. Recent experiments twisting DNA demonstrate novel phenomena precipitated by the interplay of topological and geometric properties. Using advanced mathematical and computational techniques, the project aims to explain how topological constraints and changes disturb key polymer behaviour.