  This article is a brief presentation of results surrounding the fundamental
gap. We begin by recalling Bakry-Emery geometry and demonstrate connections
between eigenvalues of the Laplacian with the Dirichlet and Neumann boundary
conditions. We then show a connection between the fundamental gap and
Bakry-Emery geometry, concluding with a presentation of the key ideas in
Andrews's and Clutterbuck's proof of the fundamental gap conjecture. We
conclude with a presentation of results for the fundamental gap of triangles
and simplices.
