Smoothing the circle

Smooth numbers, integers whose prime factors are all small, play a central role in many areas of analytic and computational number theory. The Gauss circle problem, on the other hand, concerns counting lattice points inside a large circle and understanding the error term in this count. In this talk, we will give an introduction to both of these topics, describe a new problem arising from their connection, and discuss some of the results towards these problems. The last part of this talk will be ongoing joint work with Stelios Sachpazis.