The talk will be in the general area of birational geometry. Can we find singular representatives of birational equivalence classes of algebraic varieties, with the simplest possible singularities? In particular, can we find the smallest class of singularities that necessarily persist after birational mappings that preserve smooth points and transverse self-intersections of the target spaces? Many of the questions considered were raised by Janos Kollar.

This Friday will be mandatory only for graduate students who have been a TA for strictly less than two quarters. (ie. If you were a TA for two quarters or more last year or over the summer, you do not have to come this week!) This week we will be discussing several first week of class issues including: WebWorks, the Tutoring Center, and Dealing with Difficult Classroom Situations.

Zeta functions are central topics in number theory and arithmetic algebraic geometry. They arise in many different forms. They can be viewed as generating functions for counting "points"
(or "solutions") of polynomial equations, thus contain deep arithmetic and geometric information of the equations. In this lecture, we will explain various zeta functions from this point of view, including the Riemann zeta function, the Hasse-Weil zeta function, and zeta
functions over finite fields.