I will discuss an upcoming result proving the full finite-codimension non-linear asymptotic stability of the Schwarzschild family as solutions to the Einstein vacuum equations in the exterior of the black hole region.
No symmetry is assumed. The work is based on our previous understanding of linear stability of Schwarzschild in double null gauge. Joint work with G. Holzegel, I. Rodnianski and M. Taylor.
The study of random matrix moments of moments has connections to number theory, combinatorics, and log-correlated fields. Our results give the leading order of these functions for integer moments parameters by exploiting connections with Gelfand-Tsetlin patterns and counts of lattice points in convex sets. This is joint work with Jon Keating and Theo Assiotis.