Alex Lubotzky: Sieve methods in group theory

The sieve methods are classical methods in number theory.Inspired by the 'affine sieve method' developed by Sarnak, Bourgain, Gamburd and others, as well as by works of Rivin and Kowalsky, we develop in a systemtic way a 'sieve method' for group theory. This method is especially useful for groups with 'property tau'. Hence the recent results of Breuillard-Green-Tao, Pyber-Szabo, Varju and Salehi-Golsefidy are very useful and enables one to apply them for linear groups. We will present the method and some of its applications to linear groups and to the mapping class groups. (Based on some joint papers with Chen Meiri- the first to apper soon in JAMS)