This is the first of a series of about 5 lectures (75 min each) on Deligne´s proof of the Weil Conjectures. It is intended mainly for graduate students but of course all are welcome.

I´ll try to make the first lecture colloquium style, so that hopefully even non-arithmeticians can understand the statement of this pinnacle of 20th century mathematics.

The following lectures require some basic background in algebraic geometry but if you are willing to accept the existence of a cohomology theory with good properties, you´ll actually see the complete proof. If time permits I will discuss some recent results as well.

The first lecture will be this Friday at 3.15 pm in 4N30 DRL. The schedule of the next ones will be decided at the beginning of this lecture.