The connection between discrete holomorphicity and Yang-Baxter integrability

This project will explore the fascinating and unexplained connection between two different mathematical approaches to the study of fundamental models in statistical mechanics, which underpin the modern theory of phase transitions and critical phenomena. A recent approach using simple discrete holomorphicity surprisingly recovers results obtained from the well developed theory of Yang-Baxter integrability. The discrete approach can be used to provide long awaited rigorous proofs in the theory of lattice self-avoiding walks. The connection between the two approaches will be made clear and used to further advance these fields, for which Australia has a leading international reputation.