Special Lagrangian submanifolds are submanifolds of a Ricci-flat Kahler manifold that are both minimal and Lagrangian. We will introduce some basic facts about special Lagrangian geometry and then describe a gluing construction for special Lagrangian submanifolds.

We define a new spectrum for compact length spaces and Riemannian manifolds called the ``covering spectrum" which roughly measures the size of the one dimensional holes in the space. More specifically, the covering spectrum is a set of real numbers $\delta>0$ which identify the distinct $\delta$ covers of the space. We investigate the relationship between this covering spectrum, the length spectrum, the marked length
spectrum and the Laplace spectrum. We analyze the behavior of the covering spectrum under Gromov-Hausdorff convergence and study its gap phenomenon. This is a joint work with Christina Sormani.