TITLE: A zero-density approach to smooth numbers

ABSTRACT: A number is said to be $y$-smooth if all of its prime factors are less than $y$. Such numbers appear in many places throughout analytic and combinatorial number theory, and much work has been done to investigate their distribution in arithmetic progressions and in intervals. In this talk I will try to explain the similarities and differences between studying these problems for $y$-smooth numbers and for primes. In particular, I will explain how zero-density results for Dirichlet $L$ functions can be brought to bear on the smooth number problems, even though there is no explicit formula available as in the case of primes. This approach allows one to prove results on much wider ranges of $y$ than were previously available.