Indecomposable Structure in Representation Theory and Logarithmic Conformal Field Theory

Conformal field theory furnishes a web of beautiful connections between seemingly disparate branches of pure mathematics and theoretical physics. More recently, logarithmic conformal field theory has enjoyed a resurgence in popularity, as it has been found to be necessary for describing non-local observables in condensed matter systems such as polymers and percolation. This project aims to further knowledge of the algebraic structures underpinning these logarithmic theories. Expected outcomes include an improved understanding of non-local observables in statistical systems and further beautiful connections with pure mathematics.