This paper surveys a few aspects of the global theory of wave equations. This material is structured around the contents of a minicourse given by the second author during the CMI/ETH Summer School on evolution equations during the Summer of 2008.

0 0.25 0.5 0.75 1.0 Specific review “During the summer, we like to take a mini staycation. This year it was extra special as we also got engaged. Our stay at the Biltmore was just fantastic. The service exceptional, the food amazingit was great at the pool, Wrights and also at Frank and Alberts. The only reason I am not giving it a full 5 stars is the ‘upgraded’ room was just a nice basic room....

This paper is based on two talks given by the author in the Albany meeting in the summer of The rst of these which dealt with perturbed Brownian motion and random walk is discussed in Section and the second which involved Brownian local times is the subject of Section

The proof of the conjecture mentioned in the title was finally completed in September of 1994. A. Wiles announced this result in the summer of 1993; however, there was a gap in his work. The paper of Taylor and Wiles does not close this gap but circumvents it. This article is an adaptation of several talks that I have given on this topic and is by no means about my own work. I have tried to pre...