Matt Junge (PhD student, U of Washington)

In the past decade computer science literature has studied the
effect of introducing random choices to classical processes. For example,
sequentially place n balls into n bins. For each ball, two bins are sampled
uniformly and the ball is placed in the emptier of the two. This process
does a much better job of evenly distributing the balls than the
"choiceless" version where one places each ball uniformly.

Consider the continuous version: Form a random sequence in the unit
interval by having the n*th* term be whichever of two uniformly placed
points falls in the larger gap between the previous n-1 points. I'll
confirm the intuition that this sequence is a.s. equidistributed, solving
an open problem from Itai Benjamini, Pascal Maillard and Elliot Paquette.
The history goes back a century to Weyl and more recently to Kakutani.
Several open problems will be discussed.