Bootstrap bounds on hyperbolic manifolds

The conformal bootstrap is a method for finding bounds on the scaling dimensions of operators in conformal field theories by using general consistency conditions and convex optimization. In this talk, I will discuss a version of the conformal bootstrap that can be used to obtain bounds on the eigenvalues of the Laplacian operator on hyperbolic manifolds. In two dimensions, some of these bounds are almost saturated by particular Riemann surfaces.