The primary focus of my research is logarithmic conformal field theory. Conformal field theories are quantum field theories that are invariant with respect to transformations that preserve angles but not lengths. These theories are encountered in string theory and statistical mechanics and have a very rich mathematical structure that can be described by vertex operator algebras. Logarithmic conformal field theory is a generalization of standard conformal field theory, which admits logarithmic divergences in correlation functions. The vertex operator algebras of logarithmic conformal field theories are still quite poorly understood. Here at the IPMU I hope to get a better understanding of these vertex operator algebras of logarithmic conformal field theories as well as the categorical structures underlying their representation theory.