In this talk, I review some recent results obtained for black holes using
effective field theory methods applied to quantum gravity, in particular the
unique effective action. Black holes are complex thermodynamical objects
that not only have a temperature but also have a pressure. Furthermore, they
have quantum hair which provides a solution to the black hole information
paradox.

Numerous applications in geometric, visual, and scientific computing rely on the ability to nicely distribute points in space according to a repulsive potential.  In contrast, there has been relatively little work on equidistribution of higher-dimensional geometry like curves and surfaces—which in many contexts must not pass through themselves or each other.  This talk explores methods for optimization of curve and surface geometry while avoiding (self-)collision. The starting point is the tangent-point energy of Buck & Orloff, which penalizes pairs of points that are close in space but distant with respect to geodesic distance. We develop a discretization of this energy, and introduce a novel preconditioning scheme based on a fractional Sobolev inner product.  We further accelerate this scheme via hierarchical approximation, and describe how to incorporate into a constrained optimization framework. Finally, we explore how this machinery can be applied to problems in mathematical visualization, geometric modeling, and geometry processing.