General audience presentation - Integer multiplication in time $O(n \log n)$
Integer multiplication is one of the oldest mathematical operations and still a central problem for computer arithmetic. The complexities of many other basic operations such as division, base conversion, gcds, computing $e$ and $\pi$, FFTs, etc. can be expressed in terms of the complexity of integer multiplication. In our talk, we will survey a new algorithm for multiplying two n-digit integers in time $O(n \log n)$.