In this talk I will discuss certain properties of sheaves of covacua and conformal blocks attached to modules over vertex operator algebras. After briefly recalling how these objects are constructed from a geometric point of view, I will focus on the conditions required to construct Cohomological Field Theories from these sheaves. If time permits I will also discuss open problems which naturally arise. This is based on joint works with A. Gibney and N. Tarasca.
Symbolic dynamics is the study of dynamical systems represented as infinite sequences of symbols --- these are called shift spaces. We will talk about several different types of shift spaces with varying complexity, and about how to represent a general dynamical system as a shift space.