Denis Charles (UW-Madison): The Distribution of Squarefree Smooth Integers in Short Intervals

The distribution of smooth integers (integers free of large prime factors) is an important problem with applications in pure and applied number theory. Given any real number d > 1/2, and any real number 0 < c <= 1 we show that there are numbers in the interval [X ... X + Xd] that are not divisible by any prime > Xc and are also not divisible by any perfect square.

The presentation will be informal, with a sketch of the ideas involved in the proof. We will also list some of the major open problems in this area of number theory.