Keith Ball (Warwick)

The Ribe Programme

Abstract: Following a remarkable rigidity principle discovered by M. Ribe, Bourgain proposed a programme to transfer the subtle geometric theory of finite-dimensional normed spaces to the class of general metric spaces: a programme which has had some striking successes and a number of intriguing applications to the theory of algorithms. This lecture will describe the most successful part of the programme, from the original work of Bourgain to recent developments by Mendel and Naor.