Title: Exceptional Sequences, Braid Diagrams, and the Stability Manifold of the Constructible Derived Category on $\mathbb{P}^n$

Abstract: The braid group acts on exceptional sequences and, in the special case of the constructible derived category on $\mathbb{P}^n$, this action is intimately related to that given by twists around certain spherical objects. This information can be encoded in braid diagrams. I will show how this perspective can be used to describe the stability manifold of the constructible derived category on $\mathbb{P}^n$ and to study some of its topological properties. This work is based on ongoing joint work with Jon Woolf.