**Title:** A Light in the Darkness: What Curvature has to do with Dark Matter

**Abstract:** General relativity lies at one of the most beautiful and interesting intersections of mathematics and physics. Described in the language of differential geometry, general relativity asserts that gravity is not a force but instead is an effect of the curvature of spacetime. The interplay between mathematics and physics here lends inspiration to many interesting questions in differential geometry which can often be turned back around to explain observed phenomena in the universe. One such example is the current astrophysical mystery of dark matter, which accounts for 4-5 times as much matter in the universe as regular matter, but whose nature is still largely not understood.

In this talk for the general audience, we will give a brief overview of general relativity, how dark matter may be potentially described within its framework, and how these ideas together have motivated the study of a system of geometric PDEs called the Einstein-Klein-Gordon equations. We will describe some recent results that have been found for this system in spherical symmetry as well as some natural future directions and how some of these relate back to the original motivating physical problem of dark matter.