Fundamental domains for proper affine actions of Coxeter groups in three dimensions

We study proper actions of groups $G \cong \Z/2\Z \ast \Z/2\Z \ast \Z/2\Z$ on affine space of three real dimensions. Since $G$ is nonsolvable, work of Fried and Goldman implies that it preserves a Lorentzian metric. A subgroup $\Gamma < G$ of index two acts freely, and $\R^3/\Gamma$ is a Margulis spacetime associated to a hyperbolic surface $\Sigma$. When $\Sigma$ is convex cocompact, work of Danciger, Gu{\'e}ritaud, and Kassel shows that the action of $\Gamma$ admits a polyhedral fundamental domain bounded by crooked planes. We consider under what circumstances the action of $G$ also admits a crooked fundamental domain. We show that it is possible to construct actions of $G$ that fail to admit crooked fundamental domains exactly when the extended mapping class group of $\Sigma$ fails to act transitively on the top-dimensional simplices of the arc complex of $\Sigma$. We also provide explicit descriptions of the moduli space of $G$ actions that admit crooked fundamental domains.

From Hill to Harbor: Serving Water and People on Baltimore's Civic Waterfront

People and cities alike derive their life from water. Water is consequently influenced by the actions of people and cities. This crucial relationship deserves to be commemorated, and also analyzed as further human development, sea level rise, and ecological remediation efforts influence its form. This thesis seeks to remember the past condition, recognize the current, and positively influence the future of this relationship in Baltimore’s Inner Harbor through a waterfront park and harbor history museum. How can a building and a site work together to improve the health of local hydrology while still effectively serving its human community? This thesis weaves these opportunities together to create a responsible redesign of Rash Field and Federal Hill on the south side of the Inner Harbor in Baltimore.