Joint IAS/Princeton University Number Theory Seminar

The title refers to a conjecture that Serre made in the early 1970's, that has proved to be very influential. I will sketch the main ideas of the proof of the level 1 case of Serre's conjecture. If time permits, I will indicate how these ideas can be extended to prove almost all of Serre's conjecture. The latter is joint work with J-P. Wintenberger.