Princeton University

On the Rigidity of Black Holes

Sergiu Klainerman
Princeton University
October 25, 2011

The classical result on the uniqueness of black holes in GR, due to Hawking, which asserts that regular, stationary solutions of the Einstein vacuum equations must be isometric to an admissible black hole Kerr solution, has at its core a a highly unrealistic analyticity assumption for the metric. The goal of the talk is to survey recent results, obtained in collaboration with Alexakis and Ionescu, on the general rigidity problem, without analyticity.

Serre's Conjectures on the Number of Rational Points of Bounded Height

Per Salberger
Chalmers University of Technology
April 28, 2011


We give a survey of recent results on conjectures of Heath-Brown and Serre on the asymptotic density of rational points of bounded height. The main tool in the proofs is a new global determinant method inspired by the local real and p-adic determinant methods of Bombieri-Pila and Heath-Brown.