Some Recent Developments in Combinatorics

Abstract: Over the last few years, a surprising number of extremely stubborn open problems in combinatorics have suddenly yielded. Some have been solved completely, while for others there have been leaps forward that far exceed any progress made for several decades. It is a remarkable time to be alive for a combinatorialist: in this talk I shall describe some of these recent breakthroughs and try to convey some of the excitement I (and many others) feel about them.