I will discuss recent work on the global stability of the Euler-Maxwell equations in 3D (joint work with Guo and Pausader), and of the gravity water-wave system in 2D (joint work with Pusateri).
We present practically efficient methods for proving correctness of announced results of a computation while keeping input and intermediate values information theoretically secret. These methods are applied to solve the long standing problem of preventing collusion in second-price auctions.
A continuous representation of a profinite group induces a continuous pseudorepresentation, where a pseudorepresentation is the data of the
characteristic polynomial coefficients. We discuss the geometry of the resulting map from the moduli formal groupoid of representations to the moduli formal scheme of pseudorepresentations.