Final Report Summary - EXPANDERS (Expander Graphs in Pure and Applied Mathematics)
Expander graphs are finite combinatorial objects which are sparse on one hand but very connected on the other hand. They have played a basic role in computer science in the last four decades and in the decade also in pure mathematics. The current project have made a significant contribution in both directions: on one hand we have developed a new "sieve method for non-commutative groups"- a method that enables to ask and answer questions in group theory which have not been approachable before. On the other hand we have used expanders graphs in computer science. For example, we have constructed new error correcting codes for information transition of a kind which was believed to be impossible before.
Almost 30 researchers have enjoyed the support of this grant, directly or indirectly: as PhD students, post-doc's and coauthors of the PI. Aproximately 50 reseach papers were written as part of this project. All the papers have been accepted to a very respectable journals and several of them appereared in top journals like Annals of Math., Inventiones, J. of the Amer. Math. Soc., J. of the European Math. Soc., GAFA as well as in the best computer science confrences like STOC and FOCS.
Almost 30 researchers have enjoyed the support of this grant, directly or indirectly: as PhD students, post-doc's and coauthors of the PI. Aproximately 50 reseach papers were written as part of this project. All the papers have been accepted to a very respectable journals and several of them appereared in top journals like Annals of Math., Inventiones, J. of the Amer. Math. Soc., J. of the European Math. Soc., GAFA as well as in the best computer science confrences like STOC and FOCS.