Abstract: I will give some recent examples where properly simulating and viewing mathematical objects has led to new mathematics, some of it appearing in the "Annals of Mathematics".
     I will focus on the fair allocation problem: given an infinite collection of points in the plane (a point process) how do we allocate the same area to each point in a decentralized way? See http://www.stat.berkeley.edu/~peres/stable/stable.html for one solution, and http://depts.washington.edu/probab/research.php for another.
     Different approaches to this problem have connections with probability, combinatorics, ergodic theory, the Riemann mapping theorem, and Newtonian gravity (in higher dimensions); see the gallery at http://www.math.huji.ac.il/~romik/Site/Allocations.html but there is lots of room for new creative ideas.
     I will also discuss opportunities for talented Mathematics students in the Seattle area (University of Washington and Microsoft Research).