Classical Problems in Combinatorics: Results and Conjectures
Combinatorics is rich in beautiful problems, many of which remain hopelessly out of reach for decades. Paul Erdos, who died in 1996, was the undisputed monarch of problem posers: his problems, most of which have a combinatorial flavour, have influenced large areas of mathematics.
It is fascinating that in many cases very little progress is made with a problem for decades, and then some unexpected and very beautiful ideas clear up much of the fog surrounding the problem. In my lectures I shall present several combinatorial problems, some due to Erdos, that have had such a history. In spite of the great progress with these problems, complete solutions seem to be a long way off.
My main aim is to emphasize the beauty of the proofs, and to encourage the audience to attempt the conjectures I shall present. The lectures are aimed at people with no more than an undergraduate degree: the only real requirement is mathematical maturity.